Question

solving simple quadratic equations practice
complete this assessment to review what youve learned. it will not count toward your grade.
solve the following quadratic equation using square roots. round to the nearest hundredth if necessary. \\(\frac{(x + 16)^2}{9} = 7\\). (1 point)
note: write your answer in set notation.
check answer remaining attempts: 3

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation \(\frac{(x + 16)^2}{9}=7\) by 9 to get \((x + 16)^2=7\times9 = 63\).

Step2: Take square roots

Take the square root of both sides: \(x + 16=\pm\sqrt{63}\). Simplify \(\sqrt{63}\) as \(3\sqrt{7}\approx7.94\).

Step3: Solve for x

For the positive root: \(x=- 16+\sqrt{63}\approx-16 + 7.94=-8.06\).
For the negative root: \(x=-16-\sqrt{63}\approx-16 - 7.94=-23.94\).

Answer:

\(\{-23.94, -8.06\}\)