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Simplifying 22p2 + -52p + -116 = -4 + -2p2 Reorder the terms: -116 + -52p + 22p2 = -4 + -2p2 Solving -116 + -52p + 22p2 = -4 + -2p2 Solving for variable 'p'. Reorder the terms: -116 + 4 + -52p + 22p2 + 2p2 = -4 + -2p2 + 4 + 2p2 Combine like terms: -116 + 4 = -112 -112 + -52p + 22p2 + 2p2 = -4 + -2p2 + 4 + 2p2 Combine like terms: 22p2 + 2p2 = 24p2 -112 + -52p + 24p2 = -4 + -2p2 + 4 + 2p2 Reorder the terms: -112 + -52p + 24p2 = -4 + 4 + -2p2 + 2p2 Combine like terms: -4 + 4 = 0 -112 + -52p + 24p2 = 0 + -2p2 + 2p2 -112 + -52p + 24p2 = -2p2 + 2p2 Combine like terms: -2p2 + 2p2 = 0 -112 + -52p + 24p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-28 + -13p + 6p2) = 0 Factor a trinomial. 4((-4 + -3p)(7 + -2p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -3p)' equal to zero and attempt to solve: Simplifying -4 + -3p = 0 Solving -4 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3p = 0 + 4 -3p = 0 + 4 Combine like terms: 0 + 4 = 4 -3p = 4 Divide each side by '-3'. p = -1.333333333 Simplifying p = -1.333333333Subproblem 2
Set the factor '(7 + -2p)' equal to zero and attempt to solve: Simplifying 7 + -2p = 0 Solving 7 + -2p = 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 + -2p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2p = 0 + -7 -2p = 0 + -7 Combine like terms: 0 + -7 = -7 -2p = -7 Divide each side by '-2'. p = 3.5 Simplifying p = 3.5Solution
p = {-1.333333333, 3.5}
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