8x-4=x^2+5x-14

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Solution for 8x-4=x^2+5x-14 equation:


Simplifying
8x + -4 = x2 + 5x + -14

Reorder the terms:
-4 + 8x = x2 + 5x + -14

Reorder the terms:
-4 + 8x = -14 + 5x + x2

Solving
-4 + 8x = -14 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 14 + 8x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: -4 + 14 = 10
10 + 8x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: 8x + -5x = 3x
10 + 3x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
10 + 3x + -1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
10 + 3x + -1x2 = 0 + 5x + -5x + x2 + -1x2
10 + 3x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
10 + 3x + -1x2 = 0 + x2 + -1x2
10 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 3x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(2 + x) = 0

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {5, -2}

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