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Simplifying 0 = -16x2 + 100x + 600 Reorder the terms: 0 = 600 + 100x + -16x2 Solving 0 = 600 + 100x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -600 = -600 -600 + -100x + 16x2 = 600 + 100x + -16x2 + -600 + -100x + 16x2 Reorder the terms: -600 + -100x + 16x2 = 600 + -600 + 100x + -100x + -16x2 + 16x2 Combine like terms: 600 + -600 = 0 -600 + -100x + 16x2 = 0 + 100x + -100x + -16x2 + 16x2 -600 + -100x + 16x2 = 100x + -100x + -16x2 + 16x2 Combine like terms: 100x + -100x = 0 -600 + -100x + 16x2 = 0 + -16x2 + 16x2 -600 + -100x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -600 + -100x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-150 + -25x + 4x2) = 0 Factor a trinomial. 4((-15 + -4x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-3.75, 10}
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