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

Question

.(1 point)

Answer 1

To solve the equation \((x + 16)29 = 7\), we will follow these steps:

1. First, isolate \((x + 16)\) by dividing both sides by 29:

\[ x + 16 = \frac{7}{29} \]

2. Next, subtract 16 from both sides to solve for \(x\):

\[ x = \frac{7}{29} - 16 \]

3. To perform the subtraction, we need a common denominator. The common denominator here is 29. We can rewrite 16 as \(\frac{16 \times 29}{29} = \frac{464}{29}\):

\[ x = \frac{7}{29} - \frac{464}{29} \]

4. Now, combine the fractions:

\[ x = \frac{7 - 464}{29} = \frac{-457}{29} \]

5. Finally, calculate \(-457 \div 29\):

\[ x \approx -15.759 \]

Rounding to the nearest hundredth, we get:

\[ x \approx -15.76 \]

Thus, the solution to the equation \((x + 16)29 = 7\) is:

\[ \boxed{-15.76} \]