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

Question

.(1 point)
Responses

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

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

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

{−7.5,−16.5}

Answer 1

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

1. Take the square root of both sides: \[ x + 12 = \pm 3 \]

2. This gives us two separate equations to solve: \[ x + 12 = 3 \quad \text{and} \quad x + 12 = -3 \]

3. Solve each equation for \(x\):

   • For \(x + 12 = 3\): \[ x = 3 - 12 \] \[ x = -9 \]

   • For \(x + 12 = -3\): \[ x = -3 - 12 \] \[ x = -15 \]

Thus, the solutions to the equation \((x + 12)^2 = 9\) are: \[ x = -9 \quad \text{and} \quad x = -15 \]

Therefore, the solution set is \({-9, -15}\).

The correct response is: \({-9, -15}\)