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 given quadratic equation \(-9 + \frac{(x - 3)^2}{-4} = -4\), we can start by isolating the term involving \(x\).
1. First, let's simplify the equation. We can add 9 to both sides:
\[
\frac{(x - 3)^2}{-4} = -4 + 9
\]
\[
\frac{(x - 3)^2}{-4} = 5
\]
2. Next, multiply both sides by -4 to eliminate the denominator:
\[
(x - 3)^2 = -20
\]
3. Since \((x - 3)^2\) cannot be negative, there are no real solutions to this equation. Let’s check if we might have made any mistakes in the sign or the manipulation:
- If we rewrite it again, we got \((x - 3)^2 = -20\). Since the square of a real number cannot equal a negative number, this confirms there are no real solutions.
However, since the question provides specific answers, we can double-check that the equation provided has been interpreted correctly and if it might have been structured differently. But, given the above workflow, we conclude:
- The quadratic equation has no real solutions. Thus, among the given choices, the answer is that none of them are correct due to the impossibility of obtaining real solutions from the setup.
In a misreading or different setup leading down to a quadratic offering real numbers, please provide and isolate the equation you're looking to solve, but currently, with the information and equation supplied, the result remains with no solutions.
1. First, let's simplify the equation. We can add 9 to both sides:
\[
\frac{(x - 3)^2}{-4} = -4 + 9
\]
\[
\frac{(x - 3)^2}{-4} = 5
\]
2. Next, multiply both sides by -4 to eliminate the denominator:
\[
(x - 3)^2 = -20
\]
3. Since \((x - 3)^2\) cannot be negative, there are no real solutions to this equation. Let’s check if we might have made any mistakes in the sign or the manipulation:
- If we rewrite it again, we got \((x - 3)^2 = -20\). Since the square of a real number cannot equal a negative number, this confirms there are no real solutions.
However, since the question provides specific answers, we can double-check that the equation provided has been interpreted correctly and if it might have been structured differently. But, given the above workflow, we conclude:
- The quadratic equation has no real solutions. Thus, among the given choices, the answer is that none of them are correct due to the impossibility of obtaining real solutions from the setup.
In a misreading or different setup leading down to a quadratic offering real numbers, please provide and isolate the equation you're looking to solve, but currently, with the information and equation supplied, the result remains with no solutions.