2x^2-17x+31=x^2-3x-18

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Solution for 2x^2-17x+31=x^2-3x-18 equation:


Simplifying
2x2 + -17x + 31 = x2 + -3x + -18

Reorder the terms:
31 + -17x + 2x2 = x2 + -3x + -18

Reorder the terms:
31 + -17x + 2x2 = -18 + -3x + x2

Solving
31 + -17x + 2x2 = -18 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
31 + 18 + -17x + 3x + 2x2 + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: 31 + 18 = 49
49 + -17x + 3x + 2x2 + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: -17x + 3x = -14x
49 + -14x + 2x2 + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
49 + -14x + 1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Reorder the terms:
49 + -14x + 1x2 = -18 + 18 + -3x + 3x + x2 + -1x2

Combine like terms: -18 + 18 = 0
49 + -14x + 1x2 = 0 + -3x + 3x + x2 + -1x2
49 + -14x + 1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
49 + -14x + 1x2 = 0 + x2 + -1x2
49 + -14x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
49 + -14x + 1x2 = 0

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

Subproblem 1

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {7, 7}

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