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Simplifying 2p2 + 4p + -1 = 7p2 + -7p + 1 Reorder the terms: -1 + 4p + 2p2 = 7p2 + -7p + 1 Reorder the terms: -1 + 4p + 2p2 = 1 + -7p + 7p2 Solving -1 + 4p + 2p2 = 1 + -7p + 7p2 Solving for variable 'p'. Reorder the terms: -1 + -1 + 4p + 7p + 2p2 + -7p2 = 1 + -7p + 7p2 + -1 + 7p + -7p2 Combine like terms: -1 + -1 = -2 -2 + 4p + 7p + 2p2 + -7p2 = 1 + -7p + 7p2 + -1 + 7p + -7p2 Combine like terms: 4p + 7p = 11p -2 + 11p + 2p2 + -7p2 = 1 + -7p + 7p2 + -1 + 7p + -7p2 Combine like terms: 2p2 + -7p2 = -5p2 -2 + 11p + -5p2 = 1 + -7p + 7p2 + -1 + 7p + -7p2 Reorder the terms: -2 + 11p + -5p2 = 1 + -1 + -7p + 7p + 7p2 + -7p2 Combine like terms: 1 + -1 = 0 -2 + 11p + -5p2 = 0 + -7p + 7p + 7p2 + -7p2 -2 + 11p + -5p2 = -7p + 7p + 7p2 + -7p2 Combine like terms: -7p + 7p = 0 -2 + 11p + -5p2 = 0 + 7p2 + -7p2 -2 + 11p + -5p2 = 7p2 + -7p2 Combine like terms: 7p2 + -7p2 = 0 -2 + 11p + -5p2 = 0 Factor a trinomial. (-2 + p)(1 + -5p) = 0Subproblem 1
Set the factor '(-2 + p)' equal to zero and attempt to solve: Simplifying -2 + p = 0 Solving -2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + p = 0 + 2 p = 0 + 2 Combine like terms: 0 + 2 = 2 p = 2 Simplifying p = 2Subproblem 2
Set the factor '(1 + -5p)' equal to zero and attempt to solve: Simplifying 1 + -5p = 0 Solving 1 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5p = 0 + -1 -5p = 0 + -1 Combine like terms: 0 + -1 = -1 -5p = -1 Divide each side by '-5'. p = 0.2 Simplifying p = 0.2Solution
p = {2, 0.2}
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