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}
left brace negative 7.5 comma negative 16.5 right brace
Remaining Attempts : 3

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: \[ \sqrt{(x + 12)^2} = \sqrt{9} \] This gives you: \[ x + 12 = 3 \quad \text{or} \quad x + 12 = -3 \]

2. Solve the equations:

   • From \(x + 12 = 3\): \[ x = 3 - 12 \Rightarrow x = -9 \]
   • From \(x + 12 = -3\): \[ x = -3 - 12 \Rightarrow x = -15 \]

Thus, the solutions are \(x = -9\) and \(x = -15\).

The answer is: \[ {-9, -15} \]

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