Question

values of $x$ by factoring.

$x^2 - 5x - 12 = -5x + 4$

Explanation:

Step1: Simplify the equation

First, we add \(5x\) to both sides of the equation \(x^{2}-5x - 12=-5x + 4\) to simplify it.
\(x^{2}-5x+5x - 12=-5x + 5x+4\)
Simplifying both sides, we get \(x^{2}-12 = 4\).

Step2: Rearrange to standard quadratic form

Then, we subtract 4 from both sides to get the equation in standard quadratic form \(ax^{2}+bx + c = 0\).
\(x^{2}-12-4=4 - 4\)
Which simplifies to \(x^{2}-16 = 0\).

Step3: Factor the quadratic expression

We recognize that \(x^{2}-16\) is a difference of squares, which can be factored as \((x - 4)(x + 4)=0\) (since \(a^{2}-b^{2}=(a - b)(a + b)\) and here \(a = x\), \(b = 4\) as \(x^{2}-16=x^{2}-4^{2}\)).

Step4: Solve for \(x\)

Using the zero - product property, if \((x - 4)(x + 4)=0\), then either \(x - 4=0\) or \(x + 4=0\).

• If \(x - 4=0\), then \(x=4\).
• If \(x + 4=0\), then \(x=-4\).

Answer:

The values of \(x\) are \(x = 4\) and \(x=-4\)