Question

values of x by factoring.

x² - 12x - 5 = -6x + 2

attempt 1 out of 2

Explanation:

Step1: Rearrange the equation to standard quadratic form

First, we need to get all terms on one side of the equation. Add \(6x\) to both sides and subtract \(2\) from both sides:
\(x^{2}-12x - 5+6x - 2=-6x + 2+6x - 2\)
Simplify the left - hand side and the right - hand side:
\(x^{2}-6x - 7 = 0\)

Step2: Factor the quadratic expression

We need to find two numbers that multiply to \(-7\) and add up to \(-6\). The numbers are \(-7\) and \(1\) since \((-7)\times1=-7\) and \(-7 + 1=-6\).
So, we can factor the quadratic \(x^{2}-6x - 7\) as \((x - 7)(x+1)=0\)

Step3: Solve for x using the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For \((x - 7)(x + 1)=0\), we set each factor equal to zero:

• If \(x-7=0\), then \(x = 7\)
• If \(x + 1=0\), then \(x=-1\)

Answer:

\(x = 7\) or \(x=-1\)