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Simplifying 28p2 + 164p + -224 = 0 Reorder the terms: -224 + 164p + 28p2 = 0 Solving -224 + 164p + 28p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-56 + 41p + 7p2) = 0 Factor a trinomial. 4((-7 + -1p)(8 + -7p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -1p)' equal to zero and attempt to solve: Simplifying -7 + -1p = 0 Solving -7 + -1p = 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 + -1p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1p = 0 + 7 -1p = 0 + 7 Combine like terms: 0 + 7 = 7 -1p = 7 Divide each side by '-1'. p = -7 Simplifying p = -7Subproblem 2
Set the factor '(8 + -7p)' equal to zero and attempt to solve: Simplifying 8 + -7p = 0 Solving 8 + -7p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7p = 0 + -8 -7p = 0 + -8 Combine like terms: 0 + -8 = -8 -7p = -8 Divide each side by '-7'. p = 1.142857143 Simplifying p = 1.142857143Solution
p = {-7, 1.142857143}
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