Question

solve using factoring.
$x^2 - 30x + 96 = -10x$
select the correct response:
-8, -12
8
-12
8, 12

Explanation:

Step1: Rearrange the equation

First, we need to get all terms on one side of the equation to set it to zero. Add \(10x\) to both sides:
\(x^{2}-30x + 10x+96=0\)
Simplify the \(x\) terms:
\(x^{2}-20x + 96=0\)

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(96\) and add up to \(- 20\). The numbers are \(-8\) and \(-12\) because \((-8)\times(-12) = 96\) and \(-8+( - 12)=-20\).
So we can factor the quadratic as:
\((x - 8)(x - 12)=0\)

Step3: Solve for \(x\)

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
Set \(x - 8=0\), then \(x=8\).
Set \(x - 12=0\), then \(x = 12\).

Answer:

8, 12