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Simplifying 16x(-5x + 9) = 64 Reorder the terms: 16x(9 + -5x) = 64 (9 * 16x + -5x * 16x) = 64 (144x + -80x2) = 64 Solving 144x + -80x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + 144x + -80x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 144x + -80x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-4 + 9x + -5x2) = 0 Factor a trinomial. 16((-1 + x)(4 + -5x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8Solution
x = {1, 0.8}
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