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Simplifying R(p) = -4p2 + 800p Multiply R * p pR = -4p2 + 800p Reorder the terms: pR = 800p + -4p2 Solving pR = 800p + -4p2 Solving for variable 'p'. Reorder the terms: -800p + pR + 4p2 = 800p + -4p2 + -800p + 4p2 Reorder the terms: -800p + pR + 4p2 = 800p + -800p + -4p2 + 4p2 Combine like terms: 800p + -800p = 0 -800p + pR + 4p2 = 0 + -4p2 + 4p2 -800p + pR + 4p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -800p + pR + 4p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-800 + R + 4p) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-800 + R + 4p)' equal to zero and attempt to solve: Simplifying -800 + R + 4p = 0 Solving -800 + R + 4p = 0 Move all terms containing p to the left, all other terms to the right. Add '800' to each side of the equation. -800 + R + 800 + 4p = 0 + 800 Reorder the terms: -800 + 800 + R + 4p = 0 + 800 Combine like terms: -800 + 800 = 0 0 + R + 4p = 0 + 800 R + 4p = 0 + 800 Combine like terms: 0 + 800 = 800 R + 4p = 800 Add '-1R' to each side of the equation. R + -1R + 4p = 800 + -1R Combine like terms: R + -1R = 0 0 + 4p = 800 + -1R 4p = 800 + -1R Divide each side by '4'. p = 200 + -0.25R Simplifying p = 200 + -0.25RSolution
p = {0, 200 + -0.25R}
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