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Simplifying 2p2 = -5p + 25 Reorder the terms: 2p2 = 25 + -5p Solving 2p2 = 25 + -5p Solving for variable 'p'. Reorder the terms: -25 + 5p + 2p2 = 25 + -5p + -25 + 5p Reorder the terms: -25 + 5p + 2p2 = 25 + -25 + -5p + 5p Combine like terms: 25 + -25 = 0 -25 + 5p + 2p2 = 0 + -5p + 5p -25 + 5p + 2p2 = -5p + 5p Combine like terms: -5p + 5p = 0 -25 + 5p + 2p2 = 0 Factor a trinomial. (-5 + -1p)(5 + -2p) = 0Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve: Simplifying -5 + -1p = 0 Solving -5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1p = 0 + 5 -1p = 0 + 5 Combine like terms: 0 + 5 = 5 -1p = 5 Divide each side by '-1'. p = -5 Simplifying p = -5Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve: Simplifying 5 + -2p = 0 Solving 5 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2p = 0 + -5 -2p = 0 + -5 Combine like terms: 0 + -5 = -5 -2p = -5 Divide each side by '-2'. p = 2.5 Simplifying p = 2.5Solution
p = {-5, 2.5}
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