(x^2)+(3x+2)=90

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Solution for (x^2)+(3x+2)=90 equation:


Simplifying
(x2) + (3x + 2) = 90
x2 + (3x + 2) = 90

Reorder the terms:
x2 + (2 + 3x) = 90

Remove parenthesis around (2 + 3x)
x2 + 2 + 3x = 90

Reorder the terms:
2 + 3x + x2 = 90

Solving
2 + 3x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
2 + -90 + 3x + x2 = 90 + -90

Combine like terms: 2 + -90 = -88
-88 + 3x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-88 + 3x + x2 = 0

Factor a trinomial.
(-11 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11

Subproblem 2

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

Solution

x = {-11, 8}

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