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

Answer 1

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

1. Divide both sides by 29:

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

2. Next, we subtract 16 from both sides:

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

3. To combine the two terms here (the fraction and the whole number), we convert \(16\) into a fraction with a denominator of \(29\):

   \[ 16 = \frac{16 \times 29}{29} = \frac{464}{29} \]

4. Now, we can combine the two fractions:

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

5. Now, we simplify \(\frac{-457}{29}\):

   \[ x \approx -15.76 \]

So, the solution to the equation rounded to the nearest hundredth is:

\[ \boxed{-15.76} \]