3x^2-11x-1=x-13

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Solution for 3x^2-11x-1=x-13 equation:


Simplifying
3x2 + -11x + -1 = x + -13

Reorder the terms:
-1 + -11x + 3x2 = x + -13

Reorder the terms:
-1 + -11x + 3x2 = -13 + x

Solving
-1 + -11x + 3x2 = -13 + x

Solving for variable 'x'.

Reorder the terms:
-1 + 13 + -11x + -1x + 3x2 = -13 + x + 13 + -1x

Combine like terms: -1 + 13 = 12
12 + -11x + -1x + 3x2 = -13 + x + 13 + -1x

Combine like terms: -11x + -1x = -12x
12 + -12x + 3x2 = -13 + x + 13 + -1x

Reorder the terms:
12 + -12x + 3x2 = -13 + 13 + x + -1x

Combine like terms: -13 + 13 = 0
12 + -12x + 3x2 = 0 + x + -1x
12 + -12x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
12 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -4x + x2) = 0

Factor a trinomial.
3((2 + -1x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {2, 2}

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