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Simplifying R(x) = x(72 + -4x) Multiply R * x xR = x(72 + -4x) xR = (72 * x + -4x * x) xR = (72x + -4x2) Solving xR = 72x + -4x2 Solving for variable 'x'. Reorder the terms: -72x + xR + 4x2 = 72x + -4x2 + -72x + 4x2 Reorder the terms: -72x + xR + 4x2 = 72x + -72x + -4x2 + 4x2 Combine like terms: 72x + -72x = 0 -72x + xR + 4x2 = 0 + -4x2 + 4x2 -72x + xR + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -72x + xR + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-72 + R + 4x) = 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 '(-72 + R + 4x)' equal to zero and attempt to solve: Simplifying -72 + R + 4x = 0 Solving -72 + R + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + R + 72 + 4x = 0 + 72 Reorder the terms: -72 + 72 + R + 4x = 0 + 72 Combine like terms: -72 + 72 = 0 0 + R + 4x = 0 + 72 R + 4x = 0 + 72 Combine like terms: 0 + 72 = 72 R + 4x = 72 Add '-1R' to each side of the equation. R + -1R + 4x = 72 + -1R Combine like terms: R + -1R = 0 0 + 4x = 72 + -1R 4x = 72 + -1R Divide each side by '4'. x = 18 + -0.25R Simplifying x = 18 + -0.25RSolution
x = {0, 18 + -0.25R}
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