Question

solve the equation.

\\x^2 - 12x + 32 = 0\\

\\(x = \\)
(use a comma to separate answers as needed.)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Factor the quadratic expression

$$ x^2 - 12x + 32 = 0 $$

Find two numbers that multiply to \(32\) and add up to \(-12\). These numbers are \(-8\) and \(-4\).

$$ (x - 8)(x - 4) = 0 $$

Step 2: Solve for x

Set each factor equal to zero:

$$ x - 8 = 0 \implies x = 8 $$

$$ x - 4 = 0 \implies x = 4 $$

Answer:

\(4, 8\)