x^2+8x=27+2x

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Solution for x^2+8x=27+2x equation:


Simplifying
x2 + 8x = 27 + 2x

Reorder the terms:
8x + x2 = 27 + 2x

Solving
8x + x2 = 27 + 2x

Solving for variable 'x'.

Reorder the terms:
-27 + 8x + -2x + x2 = 27 + 2x + -27 + -2x

Combine like terms: 8x + -2x = 6x
-27 + 6x + x2 = 27 + 2x + -27 + -2x

Reorder the terms:
-27 + 6x + x2 = 27 + -27 + 2x + -2x

Combine like terms: 27 + -27 = 0
-27 + 6x + x2 = 0 + 2x + -2x
-27 + 6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-27 + 6x + x2 = 0

Factor a trinomial.
(-9 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-9, 3}

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