Question

solve the equation by factoring.
$x^2 = 6x + 27$
the solution set is
(type an integer or a simplified fraction. use a comma to separate answers as needed. type eac

Explanation:

Step1: Rearrange the equation

First, we need to get all terms on one side of the equation to set it equal to zero. Subtract \(6x\) and \(27\) from both sides:
\(x^{2}-6x - 27=0\)

Step2: Factor the quadratic

We need to find two numbers that multiply to \(- 27\) and add up to \(-6\). The numbers are \(-9\) and \(3\) because \((-9)\times3=-27\) and \(-9 + 3=-6\). So we can factor the quadratic as:
\((x - 9)(x+3)=0\)

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 \(x-9=0\), we add \(9\) to both sides: \(x=9\)
• For \(x + 3=0\), we subtract \(3\) from both sides: \(x=-3\)

Answer:

\(-3,9\)