Completing the Square
2. Solve the equation by completing the square. Show your work.
x^2 – 30x = –125
Step 1: Add to both sides of the equation. (2 points)
Add 225 both sides of the equation
x^2 – 30x + 225 = –125
+ 225
x^2 - 30x + 225 = 100
Step 2: Factor the left side of the equation. Show your work. (2 points)
Hint: It is a perfect square trinomial.
x^2 - 30x + 225 = 100
Factor the left side of the equation:
(x - 15)^2 = 100
Step 3: Take the square root of both sides of the equation from Step 2. (1 point)
√(x - 15)^2 = √100
Step 4: Simplify the radical and solve for x. Show your work. (1 point)
x - 15 = + - 10
x - 15 = 10
x = 25
x - 15 = -10
x = 5
Solutions x = 25, 5
