Question

Some of the following quads like equation using square root round to the nearest hundredth if necessary and x + 27 to the second power over -6 = -3

Answer 1

To solve the equation \( \frac{(x + 27)^2}{-6} = -3 \), we'll start by isolating \( (x + 27)^2 \).

1. Multiply both sides by -6 to eliminate the fraction:

\[
(x + 27)^2 = -3 \times -6
\]

\[
(x + 27)^2 = 18
\]

2. Next, take the square root of both sides:

\[
x + 27 = \pm \sqrt{18}
\]

3. Simplify \( \sqrt{18} \):

\[
\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}
\]

4. Now, we have two possible equations:

\[
x + 27 = 3\sqrt{2} \quad \text{and} \quad x + 27 = -3\sqrt{2}
\]

5. Solve for \( x \) in both cases:

For \( x + 27 = 3\sqrt{2} \):

\[
x = 3\sqrt{2} - 27
\]

For \( x + 27 = -3\sqrt{2} \):

\[
x = -3\sqrt{2} - 27
\]

6. Now, we can calculate the numerical values, rounding to the nearest hundredth.

First, find the approximate value of \( \sqrt{2} \approx 1.414 \):

- For \( x = 3\sqrt{2} - 27 \):

\[
x \approx 3(1.414) - 27 \approx 4.242 - 27 \approx -22.758
\]

Rounded to the nearest hundredth:

\[
x \approx -22.76
\]

- For \( x = -3\sqrt{2} - 27 \):

\[
x \approx -3(1.414) - 27 \approx -4.242 - 27 \approx -31.242
\]

Rounded to the nearest hundredth:

\[
x \approx -31.24
\]

7. Summarizing the final results, we have:

\[
x \approx -22.76 \quad \text{and} \quad x \approx -31.24
\]