(9x^2-5x+14)+(7x^2-8x-44)=x

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Solution for (9x^2-5x+14)+(7x^2-8x-44)=x equation:


Simplifying
(9x2 + -5x + 14) + (7x2 + -8x + -44) = x

Reorder the terms:
(14 + -5x + 9x2) + (7x2 + -8x + -44) = x

Remove parenthesis around (14 + -5x + 9x2)
14 + -5x + 9x2 + (7x2 + -8x + -44) = x

Reorder the terms:
14 + -5x + 9x2 + (-44 + -8x + 7x2) = x

Remove parenthesis around (-44 + -8x + 7x2)
14 + -5x + 9x2 + -44 + -8x + 7x2 = x

Reorder the terms:
14 + -44 + -5x + -8x + 9x2 + 7x2 = x

Combine like terms: 14 + -44 = -30
-30 + -5x + -8x + 9x2 + 7x2 = x

Combine like terms: -5x + -8x = -13x
-30 + -13x + 9x2 + 7x2 = x

Combine like terms: 9x2 + 7x2 = 16x2
-30 + -13x + 16x2 = x

Solving
-30 + -13x + 16x2 = x

Solving for variable 'x'.

Reorder the terms:
-30 + -13x + -1x + 16x2 = x + -1x

Combine like terms: -13x + -1x = -14x
-30 + -14x + 16x2 = x + -1x

Combine like terms: x + -1x = 0
-30 + -14x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -7x + 8x2) = 0

Factor a trinomial.
2((-1 + -1x)(15 + -8x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(15 + -8x)' equal to zero and attempt to solve: Simplifying 15 + -8x = 0 Solving 15 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -8x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -8x = 0 + -15 -8x = 0 + -15 Combine like terms: 0 + -15 = -15 -8x = -15 Divide each side by '-8'. x = 1.875 Simplifying x = 1.875

Solution

x = {-1, 1.875}

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