Basic Algebra/Solving Quadratic Equations/Solving Quadratic Equations By Taking The Square Root of Both Sides

Lesson

One way to solve a quadratic is to use square root. Steps:

1. Factor a quadratic so that it is in the form $y=(x+z)^{2}$ ($z$ can be determined by completing the square)
2. Take the square root of both sides, so $x+z=\pm {\sqrt {y}}$
3. If y is 0, the square root is zero. In this case, there will only be one solution instead of two.
4. Solve for x

Example problems

Problem 1

${\begin{aligned}200&=2x^{2}+38\\162&=2x^{2}\\81&=x^{2}\\x&=\pm 9\end{aligned}}$

Problem 2

${\begin{aligned}64&=x^{2}+6x+9\\64&=(x+3)^{2}\\x+3&=\pm 8\\x&=-3\pm 8{\text{, i.e., }}x=\{-11,5\}\end{aligned}}$