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?

Answer 1

Answer:
`(x+2) = \pm 2`

Explanation:

If the given expression is,

`(x + 2)^2 - 9 = -5`

For solving this expression, By adding 9 on both sides,

`(x+2)^2 = 4`

By taking square root on both sides,

`√((x+2)^2) = √(4)`

`({(x+2)^2)^{(1)/(2) = \pm 2`
`( \text{ Because, }√(4) = \pm 2 \text { and }√(x) = x^{(1)/(2)})`

`{(x+2)^{2* (1)/(2) = \pm2`
`((a^m)^n=a^(m* n))`

`(x + 2) = \pm2`

Which is the required next step.

Answer 2

we have

`(x + 2)^(2)-9=-5`

Adds
`9` both sides

`(x + 2)^(2)-9+9=-5+9`

`(x + 2)^(2)=4`

square root both sides

`(x+2)=(+/-)√(4)\\(x+2)=(+/-)2\\x1=2-2=0 \\x2=-2-2=-4`

therefore

the answer is

the resulting equation is
`(x+2)=(+/-)2`