110+x^2=190+2x

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Solution for 110+x^2=190+2x equation:


Simplifying
110 + x2 = 190 + 2x

Solving
110 + x2 = 190 + 2x

Solving for variable 'x'.

Reorder the terms:
110 + -190 + -2x + x2 = 190 + 2x + -190 + -2x

Combine like terms: 110 + -190 = -80
-80 + -2x + x2 = 190 + 2x + -190 + -2x

Reorder the terms:
-80 + -2x + x2 = 190 + -190 + 2x + -2x

Combine like terms: 190 + -190 = 0
-80 + -2x + x2 = 0 + 2x + -2x
-80 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-80 + -2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(10 + -1x) = 0

Subproblem 1

Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-8, 10}

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