Question

quadratic by factoring.
$x^2 - 18x + 82 = 2$
attempt 1 out of 10

Explanation:

Step1: Simplify the equation

Subtract 2 from both sides of the equation \(x^{2}-18x + 82=2\) to get it in standard quadratic form \(ax^{2}+bx + c = 0\).
\(x^{2}-18x+82 - 2=2 - 2\)
\(x^{2}-18x + 80=0\)

Step2: Factor the quadratic

We need to find two numbers that multiply to \(80\) (the constant term) and add up to \(- 18\) (the coefficient of the \(x\) term). The numbers \(-8\) and \(-10\) satisfy this because \((-8)\times(-10)=80\) and \((-8)+(-10)=-18\).
So we can factor the quadratic as \((x - 8)(x - 10)=0\)

Step3: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((x - 8)(x - 10)=0\), we have:
Case 1: \(x-8 = 0\), then \(x=8\)
Case 2: \(x - 10=0\), then \(x = 10\)

Answer:

\(x = 8\) or \(x=10\)