Question

olve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)29=7.(1 point)

Answer 1

To solve the equation \((x + 16)29 = 7\), we first need to isolate the term \((x + 16)\). Here are the steps:

1. Divide both sides of the equation by 29:
\[
x + 16 = \frac{7}{29}
\]

2. Now, compute \(\frac{7}{29}\):
\[
x + 16 \approx 0.2414 \quad (\text{rounded to four decimal places})
\]

3. Next, we isolate \(x\) by subtracting 16 from both sides:
\[
x = \frac{7}{29} - 16
\]
To perform this subtraction, we convert 16 into a fraction with a denominator of 29:
\[
16 = \frac{16 \times 29}{29} = \frac{464}{29}
\]
So,
\[
x = \frac{7}{29} - \frac{464}{29} = \frac{7 - 464}{29} = \frac{-457}{29}
\]

4. Now divide \(-457\) by \(29\):
\[
x \approx -15.7586 \quad (\text{rounded to four decimal places})
\]

5. Rounding to the nearest hundredth, we find:
\[
x \approx -15.76
\]

Thus, the solution to the equation is:
\[
\boxed{-15.76}
\]