Question

solve for all values of x by factoring.
$x^2 + x - 12 = x + 4$

Explanation:

Step1: Simplify the equation

Subtract \(x + 4\) from both sides to set the equation to zero:
\(x^{2}+x - 12-(x + 4)=0\)
Simplify the left - hand side: \(x^{2}+x - 12 - x - 4 = 0\), which simplifies to \(x^{2}-16 = 0\)

Step2: Factor the quadratic expression

We recognize that \(x^{2}-16\) is a difference of squares. The formula for the difference of squares is \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(a=x\) and \(b = 4\), so \(x^{2}-16=(x + 4)(x - 4)=0\)

Step3: Solve for x

Set each factor equal to zero:

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

Answer:

\(x=-4\) or \(x = 4\)