Question

solve the equation.

\\(x - 2)(x + 5) = 8\\

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

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Expand the left side

$$ (x - 2)(x + 5) = 8 $$

$$ x^2 + 5x - 2x - 10 = 8 $$

$$ x^2 + 3x - 10 = 8 $$

Step 2: Set the equation to zero

$$ x^2 + 3x - 10 - 8 = 0 $$

$$ x^2 + 3x - 18 = 0 $$

Step 3: Factor the quadratic equation

$$ (x + 6)(x - 3) = 0 $$

Step 4: Solve for x

$$ x + 6 = 0 \implies x = -6 $$

$$ x - 3 = 0 \implies x = 3 $$

Answer:

-6, 3