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Simplifying 60x + -0.2x2 = p(x) Multiply p * x 60x + -0.2x2 = px Solving 60x + -0.2x2 = px Solving for variable 'x'. Reorder the terms: -1px + 60x + -0.2x2 = px + -1px Combine like terms: px + -1px = 0 -1px + 60x + -0.2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1p + 60 + -0.2x) = 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 '(-1p + 60 + -0.2x)' equal to zero and attempt to solve: Simplifying -1p + 60 + -0.2x = 0 Reorder the terms: 60 + -1p + -0.2x = 0 Solving 60 + -1p + -0.2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -1p + -60 + -0.2x = 0 + -60 Reorder the terms: 60 + -60 + -1p + -0.2x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1p + -0.2x = 0 + -60 -1p + -0.2x = 0 + -60 Combine like terms: 0 + -60 = -60 -1p + -0.2x = -60 Add 'p' to each side of the equation. -1p + p + -0.2x = -60 + p Combine like terms: -1p + p = 0 0 + -0.2x = -60 + p -0.2x = -60 + p Divide each side by '-0.2'. x = 300 + -5p Simplifying x = 300 + -5pSolution
x = {0, 300 + -5p}
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