-x^2+2x+18=5x-10

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Solution for -x^2+2x+18=5x-10 equation:


Simplifying
-1x2 + 2x + 18 = 5x + -10

Reorder the terms:
18 + 2x + -1x2 = 5x + -10

Reorder the terms:
18 + 2x + -1x2 = -10 + 5x

Solving
18 + 2x + -1x2 = -10 + 5x

Solving for variable 'x'.

Reorder the terms:
18 + 10 + 2x + -5x + -1x2 = -10 + 5x + 10 + -5x

Combine like terms: 18 + 10 = 28
28 + 2x + -5x + -1x2 = -10 + 5x + 10 + -5x

Combine like terms: 2x + -5x = -3x
28 + -3x + -1x2 = -10 + 5x + 10 + -5x

Reorder the terms:
28 + -3x + -1x2 = -10 + 10 + 5x + -5x

Combine like terms: -10 + 10 = 0
28 + -3x + -1x2 = 0 + 5x + -5x
28 + -3x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
28 + -3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(7 + x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Solution

x = {4, -7}

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