To solve the equation \(\frac{(x+16)^2}{9} = 7\) using square roots, follow these steps:
-
Multiply both sides by 9 to eliminate the fraction: \[ (x + 16)^2 = 63 \]
-
Take the square root of both sides. Remember to consider both the positive and negative roots: \[ x + 16 = \pm \sqrt{63} \]
-
Calculate \(\sqrt{63}\): \[ \sqrt{63} \approx 7.937 \]
-
Set up the two equations: \[ x + 16 = 7.937 \quad \text{and} \quad x + 16 = -7.937 \]
-
Solve for \(x\) in each case:
-
For the first equation: \[ x = 7.937 - 16 = -8.063 \]
-
For the second equation: \[ x = -7.937 - 16 = -23.937 \]
-
-
Round to the nearest hundredth:
- First solution: \(x \approx -8.06\)
- Second solution: \(x \approx -23.94\)
Thus, the solutions to the quadratic equation are: \[ x \approx -8.06 \quad \text{and} \quad x \approx -23.94 \]