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Solve the following quadratic equation using square roots: (−9+(x−3)2)/−4=−4

.(1 point)
Responses

{28,−22}
left brace 28 comma negative 22 right brace

{8,−2}
left brace 8 comma negative 2 right brace

{16,−10}
left brace 16 comma negative 10 right brace

{2,−8}

1 answer

Let's start with the given equation and solve it step-by-step:

Given: \[ \frac{-9 + (x - 3)^2}{-4} = -4 \]

  1. First, multiply both sides by -4 to eliminate the fraction: \[ -9 + (x - 3)^2 = 16 \]

  2. Next, add 9 to both sides: \[ (x - 3)^2 = 25 \]

  3. Now we take the square root of both sides: \[ x - 3 = 5 \quad \text{or} \quad x - 3 = -5 \]

  4. Solve for \(x\):

  • For the first equation: \[ x - 3 = 5 \implies x = 8 \]

  • For the second equation: \[ x - 3 = -5 \implies x = -2 \]

  1. Therefore, the solutions to the equation are: \[ {8, -2} \]

Thus, the answer is: \[ {8, -2} \]