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

Question

.(1 point)
{
}
Remaining Attempts : 3

Answer 1

To solve the quadratic equation \((x + 16)29 = 7\) using square roots, we first isolate the term involving \(x\).

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

2. Subtract 16 from both sides: \[ x = \frac{7}{29} - 16 \]

3. To combine the terms on the right, convert 16 to a fraction: \[ 16 = \frac{16 \times 29}{29} = \frac{464}{29} \]

4. Now combine the fractions: \[ x = \frac{7}{29} - \frac{464}{29} = \frac{7 - 464}{29} = \frac{-457}{29} \]

5. Calculate \(\frac{-457}{29}\): \[ -457 \div 29 \approx -15.76 \]

Therefore, the solution is: \[ x \approx -15.76 \]

Rounding to the nearest hundredth, the answer is: \[ \boxed{-15.76} \]