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Simplifying x2 + 14x + 22 = -1x2 + -10x + 150 Reorder the terms: 22 + 14x + x2 = -1x2 + -10x + 150 Reorder the terms: 22 + 14x + x2 = 150 + -10x + -1x2 Solving 22 + 14x + x2 = 150 + -10x + -1x2 Solving for variable 'x'. Reorder the terms: 22 + -150 + 14x + 10x + x2 + x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Combine like terms: 22 + -150 = -128 -128 + 14x + 10x + x2 + x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Combine like terms: 14x + 10x = 24x -128 + 24x + x2 + x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Combine like terms: x2 + x2 = 2x2 -128 + 24x + 2x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Reorder the terms: -128 + 24x + 2x2 = 150 + -150 + -10x + 10x + -1x2 + x2 Combine like terms: 150 + -150 = 0 -128 + 24x + 2x2 = 0 + -10x + 10x + -1x2 + x2 -128 + 24x + 2x2 = -10x + 10x + -1x2 + x2 Combine like terms: -10x + 10x = 0 -128 + 24x + 2x2 = 0 + -1x2 + x2 -128 + 24x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -128 + 24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + 12x + x2) = 0 Factor a trinomial. 2((-16 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve: Simplifying -16 + -1x = 0 Solving -16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x = 0 + 16 -1x = 0 + 16 Combine like terms: 0 + 16 = 16 -1x = 16 Divide each side by '-1'. x = -16 Simplifying x = -16Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-16, 4}
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