x^2-2x=10x-36

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Solution for x^2-2x=10x-36 equation:


Simplifying
x2 + -2x = 10x + -36

Reorder the terms:
-2x + x2 = 10x + -36

Reorder the terms:
-2x + x2 = -36 + 10x

Solving
-2x + x2 = -36 + 10x

Solving for variable 'x'.

Reorder the terms:
36 + -2x + -10x + x2 = -36 + 10x + 36 + -10x

Combine like terms: -2x + -10x = -12x
36 + -12x + x2 = -36 + 10x + 36 + -10x

Reorder the terms:
36 + -12x + x2 = -36 + 36 + 10x + -10x

Combine like terms: -36 + 36 = 0
36 + -12x + x2 = 0 + 10x + -10x
36 + -12x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
36 + -12x + x2 = 0

Factor a trinomial.
(6 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {6, 6}

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