x^2+11x+8=5x+3

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Solution for x^2+11x+8=5x+3 equation:


Simplifying
x2 + 11x + 8 = 5x + 3

Reorder the terms:
8 + 11x + x2 = 5x + 3

Reorder the terms:
8 + 11x + x2 = 3 + 5x

Solving
8 + 11x + x2 = 3 + 5x

Solving for variable 'x'.

Reorder the terms:
8 + -3 + 11x + -5x + x2 = 3 + 5x + -3 + -5x

Combine like terms: 8 + -3 = 5
5 + 11x + -5x + x2 = 3 + 5x + -3 + -5x

Combine like terms: 11x + -5x = 6x
5 + 6x + x2 = 3 + 5x + -3 + -5x

Reorder the terms:
5 + 6x + x2 = 3 + -3 + 5x + -5x

Combine like terms: 3 + -3 = 0
5 + 6x + x2 = 0 + 5x + -5x
5 + 6x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
5 + 6x + x2 = 0

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

Subproblem 1

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-5, -1}

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