X2+16x+24=0

Solve x^2 + 16x + 24 = 0.

Option 1: Quadratic formula

• a = 1, b = 16, c = 24
• Discriminant D = b^2 - 4ac = 256 - 96 = 160
• x = (-b ± sqrt(D)) / (2a) = (-16 ± sqrt(160)) / 2 = -8 ± sqrt(40) = -8 ± 2√10

So the roots are x = -8 + 2√10 and x = -8 - 2√10. Approximate: x ≈ -1.675 and x ≈ -14.325.

Option 2: Complete the square (for check) x^2 + 16x + 64 = 40 → (x + 8)^2 = 40 → x = -8 ± √40 = -8 ± 2√10.

If you need, I can show a quick substitution check.