Question

Solve by completing the square and then use the square root method to solve. x2 - 4x - 32 = 0

Answer 1

\[x^{2}-4x+4=32+4=36\]\[(x-2)^{2}=36\]\[x-2=\pm \sqrt{36} = \pm 6\]\[x=2 \pm 6\] so x=8 or x=-4

Answer 2

start by rewriting the equation to

x^2 - 4x = 32

to complete the square you need ( -4/2)^2 = 4

add 4 to both sides

x^2 - 4x + 4 = 32 +4

factor the left hand side

\[(x - 2)^2 = 36\]

take the square root of both sides

\[x - 2 = \pm \sqrt{36}\]

add 2 to both sides

\[x = 2 \pm 6\]

x = 8, -4