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

1 answer

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: \[ \boxed{-15.76} \]