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Simplifying y(x) = -16x2 + 64x Multiply y * x xy = -16x2 + 64x Reorder the terms: xy = 64x + -16x2 Solving xy = 64x + -16x2 Solving for variable 'x'. Reorder the terms: -64x + xy + 16x2 = 64x + -16x2 + -64x + 16x2 Reorder the terms: -64x + xy + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -64x + xy + 16x2 = 0 + -16x2 + 16x2 -64x + xy + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -64x + xy + 16x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-64 + y + 16x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-64 + y + 16x)' equal to zero and attempt to solve: Simplifying -64 + y + 16x = 0 Reorder the terms: -64 + 16x + y = 0 Solving -64 + 16x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 16x + 64 + y = 0 + 64 Reorder the terms: -64 + 64 + 16x + y = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 16x + y = 0 + 64 16x + y = 0 + 64 Combine like terms: 0 + 64 = 64 16x + y = 64 Add '-1y' to each side of the equation. 16x + y + -1y = 64 + -1y Combine like terms: y + -1y = 0 16x + 0 = 64 + -1y 16x = 64 + -1y Divide each side by '16'. x = 4 + -0.0625y Simplifying x = 4 + -0.0625ySolution
x = {0, 4 + -0.0625y}
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