x^2-x-22=-3x+2

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Solution for x^2-x-22=-3x+2 equation:


Simplifying
x2 + -1x + -22 = -3x + 2

Reorder the terms:
-22 + -1x + x2 = -3x + 2

Reorder the terms:
-22 + -1x + x2 = 2 + -3x

Solving
-22 + -1x + x2 = 2 + -3x

Solving for variable 'x'.

Reorder the terms:
-22 + -2 + -1x + 3x + x2 = 2 + -3x + -2 + 3x

Combine like terms: -22 + -2 = -24
-24 + -1x + 3x + x2 = 2 + -3x + -2 + 3x

Combine like terms: -1x + 3x = 2x
-24 + 2x + x2 = 2 + -3x + -2 + 3x

Reorder the terms:
-24 + 2x + x2 = 2 + -2 + -3x + 3x

Combine like terms: 2 + -2 = 0
-24 + 2x + x2 = 0 + -3x + 3x
-24 + 2x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -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 '(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

Solution

x = {-6, 4}

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