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Simplifying 5x2 + 20x + -90 = 99 + -4x2 + -16x Reorder the terms: -90 + 20x + 5x2 = 99 + -4x2 + -16x Reorder the terms: -90 + 20x + 5x2 = 99 + -16x + -4x2 Solving -90 + 20x + 5x2 = 99 + -16x + -4x2 Solving for variable 'x'. Reorder the terms: -90 + -99 + 20x + 16x + 5x2 + 4x2 = 99 + -16x + -4x2 + -99 + 16x + 4x2 Combine like terms: -90 + -99 = -189 -189 + 20x + 16x + 5x2 + 4x2 = 99 + -16x + -4x2 + -99 + 16x + 4x2 Combine like terms: 20x + 16x = 36x -189 + 36x + 5x2 + 4x2 = 99 + -16x + -4x2 + -99 + 16x + 4x2 Combine like terms: 5x2 + 4x2 = 9x2 -189 + 36x + 9x2 = 99 + -16x + -4x2 + -99 + 16x + 4x2 Reorder the terms: -189 + 36x + 9x2 = 99 + -99 + -16x + 16x + -4x2 + 4x2 Combine like terms: 99 + -99 = 0 -189 + 36x + 9x2 = 0 + -16x + 16x + -4x2 + 4x2 -189 + 36x + 9x2 = -16x + 16x + -4x2 + 4x2 Combine like terms: -16x + 16x = 0 -189 + 36x + 9x2 = 0 + -4x2 + 4x2 -189 + 36x + 9x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -189 + 36x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-21 + 4x + x2) = 0 Factor a trinomial. 9((-7 + -1x)(3 + -1x)) = 0 Ignore the factor 9.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 = -7Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-7, 3}
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