Solve x² + 14x + 17 = -96 for x.

Solution:

Given x² + 14x + 17 = -96

This is a polynomial of degree 2

Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

x² + 14x + 17 +96 =0

x² + 14x + 113 = 0

We use quadratic formula to find roots of the equation

x = {-b ± √b² - 4ac}/2a

Here a = 1; b = 14, c = 113

x = {-14 ± √(-14)² - 4(1)(113)}/2(1)

x = -14 ± √196 - 452 /2

x = -14 ± √-256 /2

x = -14 ± 16i /2

x = -7 ± 8i

Therefore, the roots are -7 ± 8i.

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Solve x² + 14x + 17 = -96 for x.

Summary:

By solving x² + 14x + 17 = -96, we get x values as -7 ± 8i.