10x-13=x^2+12

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Solution for 10x-13=x^2+12 equation:


Simplifying
10x + -13 = x2 + 12

Reorder the terms:
-13 + 10x = x2 + 12

Reorder the terms:
-13 + 10x = 12 + x2

Solving
-13 + 10x = 12 + x2

Solving for variable 'x'.

Reorder the terms:
-13 + -12 + 10x + -1x2 = 12 + x2 + -12 + -1x2

Combine like terms: -13 + -12 = -25
-25 + 10x + -1x2 = 12 + x2 + -12 + -1x2

Reorder the terms:
-25 + 10x + -1x2 = 12 + -12 + x2 + -1x2

Combine like terms: 12 + -12 = 0
-25 + 10x + -1x2 = 0 + x2 + -1x2
-25 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-25 + 10x + -1x2 = 0

Factor a trinomial.
(-5 + x)(5 + -1x) = 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 '(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

Solution

x = {5, 5}

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