Question

Solve the following quadratic equation using square roots: −9+(x−3)^2/−4 =−4 .(1 point)
Responses

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

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

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

{28,−22}

Answer 1

To solve the equation \(-9 + \frac{(x-3)^2}{-4} = -4\), we will first isolate the term involving \(x\).

1. Start by simplifying the equation:

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

Add 9 to both sides:

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

This simplifies to:

\[
\frac{(x-3)^2}{-4} = 5
\]

2. Next, multiply both sides by -4 to eliminate the fraction:

\[
(x-3)^2 = -20
\]

3. We see that the expression \((x-3)^2\) cannot equal -20 because the square of a real number is always non-negative. Hence, there are no real solutions to this quadratic equation.

Given that there are no real solutions, none of the provided multiple-choice answers \(\{8, -2\}, \{16, -10\}, \{2, -8\}, \{28, -22\}\) are correct as they represent sets of real solutions.

The conclusion is that the equation has no real solutions. In the context of the multiple-choice answers provided, the question may need clarification or revision, as all responses involve real numbers.