Question

the quadratic by factoring.
$x^2 - x + 18 = -8x + 8$

Explanation:

Step1: Rearrange the equation

First, we need to get all terms on one side of the equation to set it to zero. Add \(8x\) to both sides and subtract \(8\) from both sides:
\(x^{2}-x + 8x+18 - 8=0\)
Simplify the like - terms: \(x^{2}+7x + 10 = 0\)

Step2: Factor the quadratic

We need to find two numbers that multiply to \(10\) (the constant term) and add up to \(7\) (the coefficient of the \(x\) term). The numbers \(2\) and \(5\) satisfy this because \(2\times5 = 10\) and \(2 + 5=7\).
So we can factor the quadratic as \((x + 2)(x+5)=0\)

Step3: Solve for \(x\)

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
Set \(x + 2=0\), then \(x=-2\)
Set \(x + 5=0\), then \(x=-5\)

Answer:

\(x=-2\) or \(x = - 5\)