x^2+13x-11=5x-2

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Solution for x^2+13x-11=5x-2 equation:


Simplifying
x2 + 13x + -11 = 5x + -2

Reorder the terms:
-11 + 13x + x2 = 5x + -2

Reorder the terms:
-11 + 13x + x2 = -2 + 5x

Solving
-11 + 13x + x2 = -2 + 5x

Solving for variable 'x'.

Reorder the terms:
-11 + 2 + 13x + -5x + x2 = -2 + 5x + 2 + -5x

Combine like terms: -11 + 2 = -9
-9 + 13x + -5x + x2 = -2 + 5x + 2 + -5x

Combine like terms: 13x + -5x = 8x
-9 + 8x + x2 = -2 + 5x + 2 + -5x

Reorder the terms:
-9 + 8x + x2 = -2 + 2 + 5x + -5x

Combine like terms: -2 + 2 = 0
-9 + 8x + x2 = 0 + 5x + -5x
-9 + 8x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-9 + 8x + x2 = 0

Factor a trinomial.
(-9 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

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

Solution

x = {-9, 1}

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