Question

(x+ 16) squared / 9 = 7

Answer 1

To solve the equation \(\frac{(x + 16)^2}{9} = 7\), we can start by eliminating the fraction. Multiply both sides by 9:

\[
(x + 16)^2 = 63
\]

Next, take the square root of both sides. Remember to consider both the positive and negative roots:

\[
x + 16 = \sqrt{63} \quad \text{or} \quad x + 16 = -\sqrt{63}
\]

Now, isolate \(x\) in each case.

For the positive root:

\[
x = \sqrt{63} - 16
\]

For the negative root:

\[
x = -\sqrt{63} - 16
\]

Now, approximate \(\sqrt{63}\) if needed. Since \(63\) can be simplified to \(3\sqrt{7}\), we can either leave the answers in terms of \(\sqrt{63}\) or provide a numerical approximation.

The approximate value of \(\sqrt{63}\) is about \(7.937\), so:

1. Positive case:
\[
x \approx 7.937 - 16 \approx -8.063
\]

2. Negative case:
\[
x \approx -7.937 - 16 \approx -23.937
\]

Thus, the solutions for \(x\) are:

\[
x = \sqrt{63} - 16 \quad \text{or} \quad x = -\sqrt{63} - 16
\]

In approximate numerical form:

\[
x \approx -8.063 \quad \text{or} \quad x \approx -23.937
\]