Question

Theo started to solve the quadratic equation (x + 2)^2 – 9 = –5. He added 9 to both sides and the resulting equation was (x + 2)^2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?

x + 2 = ±4
x + 2 = ±2
x + 2 = ±8
x + 2 = ±16

Answer 1

The square root of (x + 2)² is (x + 2) .

The square roots of 4 are +2 and -2 .

So the resulting equation was x + 2 = ± 2 .

From there, it was pretty easy for Theo to find the solutions
to the original equation . . .

If (x + 2) = +2 , then x = 0 .

If (x + 2) = -2 , then x = -4 .

Answer 2

When we take the square root of each side, the equation would become:
abs (x+2) = 2
⇒ x+2 = ±2.

The final answer is x + 2 = ±2.

Hope this helps~