Question

solve ( 3w^2 + 12 = 96 ), where ( w ) is a real number. round your answer to the nearest hundredth. if there is more than one solution, separate them with commas. if there is no solution, click on
o solution\.

Explanation:

Step1: Isolate the quadratic term

Subtract 12 from both sides of the equation \(3w^{2}+12 = 96\).
\(3w^{2}=96 - 12\)
\(3w^{2}=84\)

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

Divide both sides by 3.
\(w^{2}=\frac{84}{3}\)
\(w^{2} = 28\)

Step3: Solve for \(w\)

Take the square root of both sides. Remember, a square root has two solutions (positive and negative).
\(w=\pm\sqrt{28}\)
Simplify \(\sqrt{28}\approx5.2915\), so \(w\approx\pm5.29\) (rounded to the nearest hundredth).

Answer:

\(w\approx - 5.29,5.29\)