Question

the solution to ( x^2 - 10x = 24 ) is ( \boldsymbol{12} ) or ( \boldsymbol{-2} ) (complete)
the solution to ( 2x^2 - 11 = 87 ) is (\boldsymbol{
ule{1cm}{0.15mm}}) (done)

Explanation:

Step1: Isolate the quadratic term

Start with the equation \(2x^2 - 11 = 87\). Add 11 to both sides to isolate the \(2x^2\) term.
\(2x^2 - 11 + 11 = 87 + 11\)
\(2x^2 = 98\)

Step2: Solve for \(x^2\)

Divide both sides of the equation \(2x^2 = 98\) by 2 to solve for \(x^2\).
\(\frac{2x^2}{2} = \frac{98}{2}\)
\(x^2 = 49\)

Step3: Solve for \(x\)

Take the square root of both sides. Remember that when taking the square root of a number, we consider both the positive and negative roots.
\(x = \pm\sqrt{49}\)
\(x = \pm 7\)

Answer:

\(7\) or \(-7\)