Question

solve: $7r^2 - 448 = 0$
options:
$\\{-2, -7\\}$
$\\{-2, -8\\}$
$\\{4, 8\\}$
$\\{7, 0\\}$
$\\{-8, 8\\}$

Explanation:

Step1: Isolate the quadratic term

Start with the equation \(7r^2 - 448 = 0\). Add 448 to both sides:
\(7r^2 = 448\)

Step2: Solve for \(r^2\)

Divide both sides by 7:
\(r^2 = \frac{448}{7} = 64\)

Step3: Take square roots

Take the square root of both sides. Remember, square roots have two solutions (positive and negative):
\(r = \pm\sqrt{64} = \pm 8\)

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

Answer:

\(\{-8, 8\}\)