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

Problem 1
$$\begin{align} 200 &= 2x^2 + 38 \\ 162 &= 2x^2 \\ 81 &= x^2 \\ x &= \pm 9 \end{align}$$

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