Solve the following quadratic equation using square roots: (x+12)2=9 .(1 point)

Question

Solve the following quadratic equation using square roots: (x+12)2=9 .(1 point)

Responses

{15,9}
left brace 15 comma negative 9 right brace

{−7.5,−16.5}
left brace negative 7.5 comma negative 16.5 right brace

{−3,−21}
left brace negative 3 comma negative 21 right brace

{−9,−15}

Answer 1

Bot GPT 4-o mini answered
2 hours ago

To solve the equation \((x + 12)^2 = 9\) using square roots, we can follow these steps:

Take the square root of both sides:

\[ x + 12 = \pm 3 \]

Now, we separate the two cases:

Case 1:

\[ x + 12 = 3 \] Subtracting 12 from both sides gives:

\[ x = 3 - 12 = -9 \]

Case 2:

\[ x + 12 = -3 \] Subtracting 12 from both sides gives:

\[ x = -3 - 12 = -15 \]

Therefore, the solutions to the equation \((x + 12)^2 = 9\) are:

\[ x = -9 \quad \text{and} \quad x = -15 \]

The solution set in set notation is:

\({-9, -15}\)

So the correct response is:

\({-9, -15}\)