x^2-5x-5=-8x+5

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Solution for x^2-5x-5=-8x+5 equation:


Simplifying
x2 + -5x + -5 = -8x + 5

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

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

Solving
-5 + -5x + x2 = 5 + -8x

Solving for variable 'x'.

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

Combine like terms: -5 + -5 = -10
-10 + -5x + 8x + x2 = 5 + -8x + -5 + 8x

Combine like terms: -5x + 8x = 3x
-10 + 3x + x2 = 5 + -8x + -5 + 8x

Reorder the terms:
-10 + 3x + x2 = 5 + -5 + -8x + 8x

Combine like terms: 5 + -5 = 0
-10 + 3x + x2 = 0 + -8x + 8x
-10 + 3x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-5, 2}

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