Question

Solve the following quadratic equation using square roots: (x−7)^2−9/4=0
.(1 point)
Responses

{2,−16}
left brace 2 comma negative 16 right brace

{−4,−10}
left brace negative 4 comma negative 10 right brace

{10.61,3.39}
left brace 10.61 comma 3.39 right brace

{10,4}

Answers

Answered by GPT-4o mini
To solve the equation \((x - 7)^2 - \frac{9}{4} = 0\) using square roots, follow these steps:

1. Start by isolating the squared term:
\[
(x - 7)^2 = \frac{9}{4}
\]

2. Take the square root of both sides:
\[
x - 7 = \pm \sqrt{\frac{9}{4}}
\]
\[
x - 7 = \pm \frac{3}{2}
\]

3. Now, solve for \(x\) by adding \(7\) to both sides:
- For the positive case:
\[
x = 7 + \frac{3}{2} = 7 + 1.5 = 8.5
\]
- For the negative case:
\[
x = 7 - \frac{3}{2} = 7 - 1.5 = 5.5
\]

4. Therefore, the solutions are:
\[
x = 8.5 \quad \text{and} \quad x = 5.5
\]

Since \(8.5\) and \(5.5\) do not match any provided response options, it seems either the problem has inconsistencies, or there were mistakes in the setup of options.

So the correct solutions to the equation are \(x = 8.5\) and \(x = 5.5\). None of the provided options match this result.
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions