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

Question

.(1 point)
Responses

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

{−3,−21}

Answer 1

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

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

2. Now, solve for \(x\) in two cases:

   Case 1: \[ x + 12 = 3 \] Subtract 12 from both sides: \[ x = 3 - 12 = -9 \]

   Case 2: \[ x + 12 = -3 \] Subtract 12 from both sides: \[ x = -3 - 12 = -15 \]

So, the solutions to the equation are: \[ { -9, -15 } \]

The correct response is: \({−9,−15}\) (left brace negative 9 comma negative 15 right brace).