x^2-17x+31=-3x-2

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Solution for x^2-17x+31=-3x-2 equation: 


Simplifying
x2 + -17x + 31 = -3x + -2

Reorder the terms:
31 + -17x + x2 = -3x + -2

Reorder the terms:
31 + -17x + x2 = -2 + -3x

Solving
31 + -17x + x2 = -2 + -3x

Solving for variable 'x'.

Reorder the terms:
31 + 2 + -17x + 3x + x2 = -2 + -3x + 2 + 3x

Combine like terms: 31 + 2 = 33
33 + -17x + 3x + x2 = -2 + -3x + 2 + 3x

Combine like terms: -17x + 3x = -14x
33 + -14x + x2 = -2 + -3x + 2 + 3x

Reorder the terms:
33 + -14x + x2 = -2 + 2 + -3x + 3x

Combine like terms: -2 + 2 = 0
33 + -14x + x2 = 0 + -3x + 3x
33 + -14x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
33 + -14x + x2 = 0

Factor a trinomial.
(3 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {3, 11}

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