Question

solve for (x) in the equation (x^2 + 14x + 17 = -96).

• (x = -7 pm 4sqrt{6}i)
• (x = -7 pm 8i)
• (x = 7 pm 4sqrt{6}i)
• (x = 7 pm 8i)

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Write in standard form

$$ x^2 + 14x + 17 = -96 $$

$$ x^2 + 14x + 113 = 0 $$

Step 2: Apply the quadratic formula

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ x = \frac{-14 \pm \sqrt{14^2 - 4(1)(113)}}{2(1)} $$

$$ x = \frac{-14 \pm \sqrt{196 - 452}}{2} $$

$$ x = \frac{-14 \pm \sqrt{-256}}{2} $$

Step 3: Simplify the expression

$$ x = \frac{-14 \pm 16i}{2} $$

$$ x = -7 \pm 8i $$

Answer:

\( x = -7 \pm 8i \)