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Simplifying A(p) = 80p + -4p2 Multiply A * p pA = 80p + -4p2 Solving pA = 80p + -4p2 Solving for variable 'p'. Reorder the terms: -80p + pA + 4p2 = 80p + -4p2 + -80p + 4p2 Reorder the terms: -80p + pA + 4p2 = 80p + -80p + -4p2 + 4p2 Combine like terms: 80p + -80p = 0 -80p + pA + 4p2 = 0 + -4p2 + 4p2 -80p + pA + 4p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -80p + pA + 4p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-80 + A + 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 '(-80 + A + 4p)' equal to zero and attempt to solve: Simplifying -80 + A + 4p = 0 Solving -80 + A + 4p = 0 Move all terms containing p to the left, all other terms to the right. Add '80' to each side of the equation. -80 + A + 80 + 4p = 0 + 80 Reorder the terms: -80 + 80 + A + 4p = 0 + 80 Combine like terms: -80 + 80 = 0 0 + A + 4p = 0 + 80 A + 4p = 0 + 80 Combine like terms: 0 + 80 = 80 A + 4p = 80 Add '-1A' to each side of the equation. A + -1A + 4p = 80 + -1A Combine like terms: A + -1A = 0 0 + 4p = 80 + -1A 4p = 80 + -1A Divide each side by '4'. p = 20 + -0.25A Simplifying p = 20 + -0.25ASolution
p = {0, 20 + -0.25A}
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