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Simplifying 0 = 6p2 + 1800p + -2400000 Reorder the terms: 0 = -2400000 + 1800p + 6p2 Solving 0 = -2400000 + 1800p + 6p2 Solving for variable 'p'. Combine like terms: 0 + 2400000 = 2400000 2400000 + -1800p + -6p2 = -2400000 + 1800p + 6p2 + 2400000 + -1800p + -6p2 Reorder the terms: 2400000 + -1800p + -6p2 = -2400000 + 2400000 + 1800p + -1800p + 6p2 + -6p2 Combine like terms: -2400000 + 2400000 = 0 2400000 + -1800p + -6p2 = 0 + 1800p + -1800p + 6p2 + -6p2 2400000 + -1800p + -6p2 = 1800p + -1800p + 6p2 + -6p2 Combine like terms: 1800p + -1800p = 0 2400000 + -1800p + -6p2 = 0 + 6p2 + -6p2 2400000 + -1800p + -6p2 = 6p2 + -6p2 Combine like terms: 6p2 + -6p2 = 0 2400000 + -1800p + -6p2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(400000 + -300p + -1p2) = 0 Factor a trinomial. 6((500 + -1p)(800 + p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(500 + -1p)' equal to zero and attempt to solve: Simplifying 500 + -1p = 0 Solving 500 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-500' to each side of the equation. 500 + -500 + -1p = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -1p = 0 + -500 -1p = 0 + -500 Combine like terms: 0 + -500 = -500 -1p = -500 Divide each side by '-1'. p = 500 Simplifying p = 500Subproblem 2
Set the factor '(800 + p)' equal to zero and attempt to solve: Simplifying 800 + p = 0 Solving 800 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-800' to each side of the equation. 800 + -800 + p = 0 + -800 Combine like terms: 800 + -800 = 0 0 + p = 0 + -800 p = 0 + -800 Combine like terms: 0 + -800 = -800 p = -800 Simplifying p = -800Solution
p = {500, -800}
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