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Simplifying 10x2 + -16 = 4 + -5x2 + -20x Reorder the terms: -16 + 10x2 = 4 + -5x2 + -20x Reorder the terms: -16 + 10x2 = 4 + -20x + -5x2 Solving -16 + 10x2 = 4 + -20x + -5x2 Solving for variable 'x'. Reorder the terms: -16 + -4 + 20x + 10x2 + 5x2 = 4 + -20x + -5x2 + -4 + 20x + 5x2 Combine like terms: -16 + -4 = -20 -20 + 20x + 10x2 + 5x2 = 4 + -20x + -5x2 + -4 + 20x + 5x2 Combine like terms: 10x2 + 5x2 = 15x2 -20 + 20x + 15x2 = 4 + -20x + -5x2 + -4 + 20x + 5x2 Reorder the terms: -20 + 20x + 15x2 = 4 + -4 + -20x + 20x + -5x2 + 5x2 Combine like terms: 4 + -4 = 0 -20 + 20x + 15x2 = 0 + -20x + 20x + -5x2 + 5x2 -20 + 20x + 15x2 = -20x + 20x + -5x2 + 5x2 Combine like terms: -20x + 20x = 0 -20 + 20x + 15x2 = 0 + -5x2 + 5x2 -20 + 20x + 15x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -20 + 20x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 4x + 3x2) = 0 Factor a trinomial. 5((-2 + -1x)(2 + -3x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-2, 0.6666666667}
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