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Simplifying 0 = 84 + -28p2 + -184p Reorder the terms: 0 = 84 + -184p + -28p2 Solving 0 = 84 + -184p + -28p2 Solving for variable 'p'. Combine like terms: 0 + -84 = -84 -84 + 184p + 28p2 = 84 + -184p + -28p2 + -84 + 184p + 28p2 Reorder the terms: -84 + 184p + 28p2 = 84 + -84 + -184p + 184p + -28p2 + 28p2 Combine like terms: 84 + -84 = 0 -84 + 184p + 28p2 = 0 + -184p + 184p + -28p2 + 28p2 -84 + 184p + 28p2 = -184p + 184p + -28p2 + 28p2 Combine like terms: -184p + 184p = 0 -84 + 184p + 28p2 = 0 + -28p2 + 28p2 -84 + 184p + 28p2 = -28p2 + 28p2 Combine like terms: -28p2 + 28p2 = 0 -84 + 184p + 28p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 46p + 7p2) = 0 Factor a trinomial. 4((-7 + -1p)(3 + -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 '(3 + -7p)' equal to zero and attempt to solve: Simplifying 3 + -7p = 0 Solving 3 + -7p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7p = 0 + -3 -7p = 0 + -3 Combine like terms: 0 + -3 = -3 -7p = -3 Divide each side by '-7'. p = 0.4285714286 Simplifying p = 0.4285714286Solution
p = {-7, 0.4285714286}
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