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Simplifying 0 = -16x2 + 20x + 300 Reorder the terms: 0 = 300 + 20x + -16x2 Solving 0 = 300 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -300 = -300 -300 + -20x + 16x2 = 300 + 20x + -16x2 + -300 + -20x + 16x2 Reorder the terms: -300 + -20x + 16x2 = 300 + -300 + 20x + -20x + -16x2 + 16x2 Combine like terms: 300 + -300 = 0 -300 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -300 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -300 + -20x + 16x2 = 0 + -16x2 + 16x2 -300 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -300 + -20x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-75 + -5x + 4x2) = 0 Factor a trinomial. 4((-15 + -4x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -4x)' equal to zero and attempt to solve: Simplifying -15 + -4x = 0 Solving -15 + -4x = 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 + -4x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4x = 0 + 15 -4x = 0 + 15 Combine like terms: 0 + 15 = 15 -4x = 15 Divide each side by '-4'. x = -3.75 Simplifying x = -3.75Subproblem 2
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 = 5Solution
x = {-3.75, 5}
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