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Solve for X Calculator + Online Solver With Free Steps
The Solve For X Calculator is an online tool that is very helpful in finding the values for x in the given mathematical expression. When variables and numbers are combined using various operations, it results in a mathematical expression.
Mathematical expressions are very important for fields like physics and engineering. They can be representations of any shape, a way to find the area and volume of any region. As variables are involved, these expressions are solved to get their values, which ultimately helps in finding the solution to the various mathematical problems.
The calculator evaluates the values for variables in each mathematical expression using different methods depending on the type of expression.
What Is the Solve for X Calculator?
The Solve For X Calculator is an online calculator that can be used to determine the roots of mathematical equations by solving them at a rate of knots.
Mathematical equations have a wide variety of types. The most commonly used are linear, quadratic, and higher degree polynomials. There is a whole bunch of techniques to solve these equations.
The important step is to select a technique to solve the given equation among a list of available options. There doesn’t need to be one method that can solve all types of equations. Also, it is possible at the same time that there are multiple solving methods for a single equation.
Therefore, it depends on the nature of the equation to choose a suitable technique. One must have a good understanding of mathematical equations and prior knowledge of different techniques to solve these equations manually.
To find the solution to such equations, you have to go through a complicated procedure that is an exhaustive and time-intensive task. You might end up with the wrong solution and you have to perform the same process again and again.
Here is the solution to all these problems. You can use Solve for X calculator, which gives relief from the painful job of solving equations. It is a simple and easy-to-understand tool that you can operate on your device just by using the browser.
How To Use the Solve for X Calculator?
You can use the Solve For X Calculator by inserting the input equation for which you want the solution. You don’t need to specify the type of equation and its solution technique, the tool will do it for you.
There is a step-by-step procedure given below to use this calculator. You must follow these steps to get the best results.
Step 1
Input the target equation. It should be a valid equation having a variable x. Put the equation in the field named Enter the equation. It can be linear, quadratic, higher degree polynomial, and trigonometric function of x.
Step 2
After entering the equation, press the Solve button to get the final answer.
Result
The result will be the values for x that satisfies the input equation. The result may vary from problem to problem.
For mathematical equations, the number of values will be equal to the highest degree in the equation. For example, if we enter a quadratic equation, it will give two roots of x.
On the other hand, for the trigonometric functions, our calculator gives answers in the form of periodical values (multiples). For instance, if the function is sin(x), it gives an answer like x = n$\pi$ where n $\in$ Z.
How Does the Solve for X Calculator Work?
The Solve for X calculator works by applying the various equation-solving techniques depending on the nature of the equations to find the values of the involved variable.
Therefore, it solves the equation according to its type to find the unknown variable.
There are different methods to solve the above-mentioned algebraic equations, but we should know about these equations first.
What Is a Linear Equation?
A Linear equation is an equation in which the unknown variable has power equal to one. This equation has only one root, which means that it has only one solution. When representing graphically, it has to be a straight line either vertically or horizontally.
The linear equation is of the form:
ax + b = 0
What Is a Quadratic Equation?
Quadratic equations are second-order algebraic equations which mean in these equations the highest power of an unknown variable is equal to two. Since the word quad means square, these equations have two solutions for the required variable.
The standard quadratic equation is given as:
\[ ax^2 + bx + c = 0 \]
The graph for quadratic equations is Parabola shaped either in the upward or downward direction depending on the maximum and minimum values of the quadratic expression.
What Are Higher-order Equations?
Higher-order Algebraic equations are equations in which the variable has a power greater than two. Some examples of higher-order equations are Cubic ($x^3$), Bi-Quadratic ($x^4$), etc.
The standard form of higher-order equation is:
\[ ax^n + bx^{n-1} + c = 0 \]
After discussing the types of equations, let us now discuss the methods to solve these equations. As mentioned above, the working of this calculator depends on any of these methods.
Method To Solve Linear Equations
Linear equations are the easiest to solve. Separate all the unknown variables on one side of the equation and constant terms on the other side by adding or subtracting the constants.
Then solve the constant terms by doing mathematical operations. After this, remove all the coefficients with the variables by multiplying or dividing them into both sides of the equation. Again simplify the equation for the desired variable.
Methods To Solve Quadratic Equations
The Quadratic Equation has two roots and these roots can be found by solving them for unknown variables. There are three different methods to solve these equations.
Factorization
Factorization is the simplest method to Solve Quadratic Equations. Factorization consists of different steps. For Factorization, we first have to convert the given equation into standard form.
\[ ax^2 + bx + c = 0 \]
Then we have to apply a mid-term break method, which means to break the middle term into two terms such that the addition of these two terms results in the original term and multiplying these two terms results in the constant term.
Then to make the required factors, take out the common term from the available terms. To find out the two required roots, simplify these obtained factors.
Quadratic Formula
There are quadratic equations that are not solvable through Factorization. So for such types of equations, Quadratic Formula will be used. To use the Quadratic Formula, first convert the quadratic equation into standard form. The Quadratic Formula is given as:
\[ x= \frac {-b \pm \sqrt{b^2-4ac}}{2a} \]
In the above equation, c belongs to the constant term in the equation, whereas a and b are the coefficients of an unknown variable. To find out the roots of the equation, just simply put the values in the formula and we will have the answer.
Method of Completing the Square
Method of Completing the Square involves squaring the equation and simplifying it to find the solution of the given equation. To understand this method, consider the standard form of the quadratic equation.
This method involves some steps. First, divide the whole equation by the coefficient of $ x^2 $. Separate the constant term by shifting it to the right side of the equation.
Now here is the main concept. We have to complete the square on the left side of the equation by keeping in mind the formula $ (a+b)^2$. This can be done by adding appropriate terms on both sides of the equation. After completing the square, take the square root on both sides of the equation, then simplify the equation to get the value of a required variable.
Methods To Solve Higher-order Equations
Higher-order equations have degrees equal to three or more and depending on the degree; these equations have three or more roots. Solving the higher-order equation is a very tedious task. Here are some methods to solve these equations.
Recognizing Factors
Take out the common term from the whole equation to convert it into quadratic form, then solve this Quadratic equation by factoring or using the quadratic formula.
Synthetic Division
Some Higher-order Equations are not solvable by recognizing the factors. So for this, we use the Synthetic division method.
It is a technique in which a higher-order polynomial is divided by a first-order polynomial using coefficients only and the sign of the divisor term is changed so that after subtraction we can get a new lower-order polynomial.
Solved Examples
The solved examples from this calculator are demonstrated below:
Example 1
Find out the roots for the following quadratic equation:
\[ x^2 – 18x + 45 =0 \]
Solution
As the input equation is quadratic, the calculator finds out two values of x, which are given as:
x1 = 3
x2 = 15
Example 2
Determine the values of x for the given 4th-degree polynomial:
\[ x^4 – 2x^3 + 6x^2+8x-40 = 0 \]
Use the Solve For X Calculator to find values.
Solution
For the 4th-degree polynomial, we get four values for x.
x{1,2} = $\pm$ 2
x3 = 1 – 3i
x4 = 1 + 3i
Example 3
Consider the below-mentioned trigonometric functions:
f(x) = 5 + 2sin(x)
Find values using the calculator above.
Solution
Once you press the Solve button you get the following results. Now for a trigonometric function, it gives periodic values (multiples of 2$\pi$).
\[ x_1 = 2 \pi n \, – \, sin^{-1}(\frac{5}{2}) \quad and \; n \in \mathbb{Z} \]
\[ x_2 = 2 \pi n + \pi \, – \, sin^{-1}(\frac{5}{2}) \quad and \; n \in \mathbb{Z} \]