Question
Solve the following quadratic equation using square roots: −9+(x−3)^2/ −4 =−4
.(1 point)
Responses
{2,−8}
left brace 2 comma negative 8 right brace
{28,−22}
left brace 28 comma negative 22 right brace
{16,−10}
left brace 16 comma negative 10 right brace
{8,−2}
.(1 point)
Responses
{2,−8}
left brace 2 comma negative 8 right brace
{28,−22}
left brace 28 comma negative 22 right brace
{16,−10}
left brace 16 comma negative 10 right brace
{8,−2}
Answers
Answered by
GPT-4o mini
To solve the equation \(-9 + \frac{(x - 3)^2}{-4} = -4\), let's first manipulate it step-by-step.
1. Start by moving \(-9\) to the right side of the equation:
\[
\frac{(x - 3)^2}{-4} = -4 + 9
\]
Simplifying the right side gives:
\[
\frac{(x - 3)^2}{-4} = 5
\]
2. Next, we can multiply both sides by \(-4\) to eliminate the fraction (note that this will flip the sign):
\[
(x - 3)^2 = -20
\]
3. Now, since we have a negative number on the right side, we note that it is impossible for a square to equal a negative number in the realm of real numbers. Therefore, there are no real solutions to this quadratic equation.
Given the choices provided, none of them represent solutions for the equation since the equation has no real roots.
In conclusion: the equation has no real solutions.
1. Start by moving \(-9\) to the right side of the equation:
\[
\frac{(x - 3)^2}{-4} = -4 + 9
\]
Simplifying the right side gives:
\[
\frac{(x - 3)^2}{-4} = 5
\]
2. Next, we can multiply both sides by \(-4\) to eliminate the fraction (note that this will flip the sign):
\[
(x - 3)^2 = -20
\]
3. Now, since we have a negative number on the right side, we note that it is impossible for a square to equal a negative number in the realm of real numbers. Therefore, there are no real solutions to this quadratic equation.
Given the choices provided, none of them represent solutions for the equation since the equation has no real roots.
In conclusion: the equation has no real solutions.