Question

solve: $5r^2 - 320 = 0$; options: {-8,7}, {8,-6}, {-8,-3}, {-8,3}, {-8,8}

Explanation:

Step1: Isolate the squared term

Start with the equation \(5r^{2}-320 = 0\). Add 320 to both sides:
\(5r^{2}=320\)

Step2: Solve for \(r^{2}\)

Divide both sides by 5:
\(r^{2}=\frac{320}{5}=64\)

Step3: Take square roots

Take the square root of both sides. Remember, square roots have two solutions (positive and negative):
\(r=\pm\sqrt{64}=\pm8\)

So the solution set is \(\{-8, 8\}\).

Answer:

\(\{-8, 8\}\) (matching the last option shown, likely labeled as \(\{-8, 8\}\) in the choices)