5x+16=x^2-8

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Solution for 5x+16=x^2-8 equation:


Simplifying
5x + 16 = x2 + -8

Reorder the terms:
16 + 5x = x2 + -8

Reorder the terms:
16 + 5x = -8 + x2

Solving
16 + 5x = -8 + x2

Solving for variable 'x'.

Reorder the terms:
16 + 8 + 5x + -1x2 = -8 + x2 + 8 + -1x2

Combine like terms: 16 + 8 = 24
24 + 5x + -1x2 = -8 + x2 + 8 + -1x2

Reorder the terms:
24 + 5x + -1x2 = -8 + 8 + x2 + -1x2

Combine like terms: -8 + 8 = 0
24 + 5x + -1x2 = 0 + x2 + -1x2
24 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 5x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(3 + x) = 0

Subproblem 1

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {8, -3}

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