Question

what are the solutions of (x^2 + 6x - 6 = 10)?

• (x = -11) or (x = 1)
• (x = -11) or (x = -1)
• (x = -8) or (x = -2)
• (x = -8) or (x = 2)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Set the equation to zero

$$ x^2 + 6x - 6 = 10 $$

Subtract \(10\) from both sides:

$$ x^2 + 6x - 16 = 0 $$

Step 2: Factor the quadratic expression

Find two numbers that multiply to \(-16\) and add to \(6\):

• The numbers are \(8\) and \(-2\).

$$ (x + 8)(x - 2) = 0 $$

Step 3: Solve for x

Set each factor to zero:

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

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

Answer:

\(x = -8\) or \(x = 2\)