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Simplifying 0 = 48x2 + -200x + 200 Reorder the terms: 0 = 200 + -200x + 48x2 Solving 0 = 200 + -200x + 48x2 Solving for variable 'x'. Combine like terms: 0 + -200 = -200 -200 + 200x + -48x2 = 200 + -200x + 48x2 + -200 + 200x + -48x2 Reorder the terms: -200 + 200x + -48x2 = 200 + -200 + -200x + 200x + 48x2 + -48x2 Combine like terms: 200 + -200 = 0 -200 + 200x + -48x2 = 0 + -200x + 200x + 48x2 + -48x2 -200 + 200x + -48x2 = -200x + 200x + 48x2 + -48x2 Combine like terms: -200x + 200x = 0 -200 + 200x + -48x2 = 0 + 48x2 + -48x2 -200 + 200x + -48x2 = 48x2 + -48x2 Combine like terms: 48x2 + -48x2 = 0 -200 + 200x + -48x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + 25x + -6x2) = 0 Factor a trinomial. 8((-5 + 2x)(5 + -3x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {2.5, 1.666666667}
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