Question

solve for all values of x by factoring.

x² - 12x - 5 = -6x + 2

answer attempt 2 out of 2

+ additional solution - no solution

x =

you have up to 3 questions left to raise your score.

Explanation:

Step1: Rearrange the equation

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

Step2: Factor the quadratic equation

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

Step3: Solve for \(x\)

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So, we set each factor equal to zero:

• For \(x - 7=0\), we add \(7\) to both sides: \(x=7\)
• For \(x + 1=0\), we subtract \(1\) from both sides: \(x=-1\)

Answer:

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