Completing Square Calculator
Completing Square Calculator solves the quadratic equation easily in a short span of eye. Simply put the polynomial or quadratic expression in the input fields and click on the calculate button next to the input section to check the accurate results.
Completing Square Calculator: Trying to find the complete squares of a quadratic equation? Don't worry you can learn how to find the complete squares in a simpler manner. We are here to assist you in getting the variable value in quadratic equations using completing square method. Want to learn more about the Completing Square Calculator then go with the below segments and get the complete details.
Procedure to Solve Quadratic Equation using Completing Squares
Completing the squares method is used to solve the quadratic equations. The general form of quadratic equation is ax2 + bx + c = 0. Go through the below sections and find the simple steps to solve the quadratic equation.
- Take any quadratic equation
- If a is not equal to 1, then divide the equation by the coefficient of x2 on both sides.
- Eliminate b term by adding or subtracting any number.
- Take half of the x term and square it.
- The equation wil be in the form of (a+b)2 or (a-b)2.
- Rewrite the perfect squares on one side.
- Combine the terms.
- Take the square root on both sides.
- Solve the equation further to get the variable value.
Example
Question: Solve 2x2 − 12x + 7 = 0 using completing squares method?
Solution:
Given equation is 2x2 − 12x + 7 = 0
a = 2, b = -12, c = 7
Divide the both sides of equation by 2
(2x2 − 12x + 7)/2 = 0/2
x2 - 6x + 7/2 = 0
x2 - 6x = -7/2
Take half of the x term and square it.
(−6* 1/2)2 = 9
Add 9 on both sides.
x2 - 6x + 9 = -7/2 + 9
(x-3)2 = (-7 + 18)/2
(x-3)2 = 11/2
Take the square root on both sides
√(x-3)2 = √11/2
x - 3 = ±√11/2
x = ±√(11/2) + 3
x = 3 + √11/2, 3 - √11/2
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FAQs on Completing Square Calculator
1. How do you solve the equation by completing the square?
You have to enter the quadratic equation in the input section and press on the calculate button to get the variable values using complete square method.
2. Why is it called completing the square?
This process is called completing square because we add a term to convert the quadratic expression into something that factors as the square of the binomial. So that the expression will become a perfect square binomial.
3. Find the complete squares in x2 − 4x + 5y2 + 10y + 14?
For this type of polynomials, we have to represent it in the form of perfect squares.
Add and subtract 4
x2 − 4x + 5y2 + 10y + 14 = x2 − 4x + 5y2 + 10y + 14 + 4 - 4
Complete the square
(x2 − 4x + 4) + 5y2 + 10y + 10 = (x - 2)2 + 5y2 + 10y + 10
Add and subtract 5
(x - 2)2 + (5y2 + 10y + 5) + 10 - 5 = (x - 2)2 + 5(y2 + 2y + 1) + 5
x2 − 4x + 5y2 + 10y + 14 = (x - 2)2 + 5(y + 1)2 + 5
4. Why is completing squares important?
You can solve any quadratic equation by factoring or using the quadratic formula. But Completing Squares process that solves the equation at a faster pace. It can solve the quadratic equation that the quadratic formula cannot.