Question

solve for (x) in the equation (x^2 + 4x - 4 = 8).

• (x = -6) or (x = 2)
• (x = -2 pm 2sqrt{2})
• (x = -2) or (x = 6)
• (x = 2 pm 2sqrt{2})

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Write in standard form

$$ x^2 + 4x - 4 = 8 $$

$$ x^2 + 4x - 12 = 0 $$

Step 2: Factor the quadratic equation

Find two numbers that multiply to \(-12\) and add to \(4\):

$$ 6 \text{ and } -2 $$

$$ (x + 6)(x - 2) = 0 $$

Step 3: Solve for x

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

$$ x - 2 = 0 \implies x = 2 $$

Answer:

\(x = -6 \text{ or } x = 2\)