What you will learn in this mini lessonYou will learn how to solve Quadratic Equations in Standard Form by Completing the Square. Our Step by Step Calculator allows you to Complete the Square and Solve your own quadratic equation.
2x2 -12x+16 Factor out 2:
= 2(x2 -6x+8)
= 2(x-3)2 -2 since 2(x-3)2 = 2x2-12x+18
To find Zeros: 2(x-3)2 = 2
(x-3)2 = 1 Take Square Root
(x-3) = ±1 Solve now
x=4 and x=2 . That’s all 😉
Solve A Quadratic Equation by Completing the SquareThe Quadratic Equation in Standard Form is
y=x²+bx+cTo Solve by Completing the Square we add and subtract
(b/2)² which yields:
y=x²+bx+ (b/2)² + c - (b/2)²Completing the Square yields:
y=(x+b/2)² + c - (b/2)²which is the Complete the Square Formula.
Example: Solve A Quadratic Equation by Completing the Square
We are given the Quadratic Equation below in Standard Form
y=x²- 6x-7 .
First, add and subtract
(- b/( 2a)²= (-(-6)/(2*1))² = 3²=9 .
Thus, we have:
y=(x²- 6x+ 9)-7- 9
This allows us to Solve via Completing the Square:
To solve (x-3)²-16 =0 we first add 16:
(x-3)²=16 . Next, we take the Square Root:
x-3 = ±4 . Adding 3 to ±4 yields the 2 solutions:
x=7 , x=-1 .
Easy, wasn’t it?
Tip: When using the Complete the Square Solver to solve
x²-6x-7=0 we must enter the 3 coefficients as
a=1, b=-6and c=-7.
Then, the Solver will first Complete the Square to find the Vertex
Thus, the Vertex Form of the Parabola is y=(x-3)²-16 .
Solving (x-3)²-16=0 yields the two zeros: x=7 , x=-1 .
Get it now? Try the above Complete the Square Solver again or check out it this excellent Step by Step Complete the Square video: