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Simplifying 6p2 = 11p + 7 Reorder the terms: 6p2 = 7 + 11p Solving 6p2 = 7 + 11p Solving for variable 'p'. Reorder the terms: -7 + -11p + 6p2 = 7 + 11p + -7 + -11p Reorder the terms: -7 + -11p + 6p2 = 7 + -7 + 11p + -11p Combine like terms: 7 + -7 = 0 -7 + -11p + 6p2 = 0 + 11p + -11p -7 + -11p + 6p2 = 11p + -11p Combine like terms: 11p + -11p = 0 -7 + -11p + 6p2 = 0 Factor a trinomial. (-1 + -2p)(7 + -3p) = 0Subproblem 1
Set the factor '(-1 + -2p)' equal to zero and attempt to solve: Simplifying -1 + -2p = 0 Solving -1 + -2p = 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 + -2p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2p = 0 + 1 -2p = 0 + 1 Combine like terms: 0 + 1 = 1 -2p = 1 Divide each side by '-2'. p = -0.5 Simplifying p = -0.5Subproblem 2
Set the factor '(7 + -3p)' equal to zero and attempt to solve: Simplifying 7 + -3p = 0 Solving 7 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3p = 0 + -7 -3p = 0 + -7 Combine like terms: 0 + -7 = -7 -3p = -7 Divide each side by '-3'. p = 2.333333333 Simplifying p = 2.333333333Solution
p = {-0.5, 2.333333333}
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