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? \bigcirc $x + 2 = \pm 4$ \bigcirc $x + 2 = \pm 2$ \bigcirc $x + 2 = \pm 8$ \bigcirc $x + 2 = \pm 16$

Explanation:

Step1: Recall square root property

For an equation \(y^2 = a\) (where \(a\geq0\)), the solutions are \(y=\pm\sqrt{a}\).
Here, we have the equation \((x + 2)^2=4\). Let \(y=x + 2\) and \(a = 4\).

Step2: Apply square root to both sides

Taking the square root of both sides of \((x + 2)^2=4\), we get \(x + 2=\pm\sqrt{4}\).
Since \(\sqrt{4}=2\), the equation becomes \(x + 2=\pm2\).

Answer:

\(x + 2=\pm2\) (corresponding to the option: \(x + 2=\pm2\))