8=x^2+x-22

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Solution for 8=x^2+x-22 equation:


Simplifying
8 = x2 + x + -22

Reorder the terms:
8 = -22 + x + x2

Solving
8 = -22 + x + x2

Solving for variable 'x'.

Combine like terms: 8 + 22 = 30
30 + -1x + -1x2 = -22 + x + x2 + 22 + -1x + -1x2

Reorder the terms:
30 + -1x + -1x2 = -22 + 22 + x + -1x + x2 + -1x2

Combine like terms: -22 + 22 = 0
30 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
30 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
30 + -1x + -1x2 = 0 + x2 + -1x2
30 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + x) = 0

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Solution

x = {5, -6}

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