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

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

$(x+2)=(+/-)\sqrt{4}\\(x+2)=(+/-)2\\x1=2-2=0 \\x2=-2-2=-4$

therefore

the answer is

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

Answer 2

Answer:  $(x+2) = \pm 2$

Step-by-step 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,

$\sqrt{(x+2)^2} = \sqrt{4}$

$({(x+2)^2)^{\frac{1}{2} = \pm 2$                    $( \text{ Because, }\sqrt{4} = \pm 2 \text { and }\sqrt{x} = x^{\frac{1}{2}})$

${(x+2)^{2\times \frac{1}{2} = \pm2$              $((a^m)^n=a^{m\times n})$

$(x + 2) = \pm2$

Which is the required next step.