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Simplifying 105p2 + -112p + -42 = 7 Reorder the terms: -42 + -112p + 105p2 = 7 Solving -42 + -112p + 105p2 = 7 Solving for variable 'p'. Reorder the terms: -42 + -7 + -112p + 105p2 = 7 + -7 Combine like terms: -42 + -7 = -49 -49 + -112p + 105p2 = 7 + -7 Combine like terms: 7 + -7 = 0 -49 + -112p + 105p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + -16p + 15p2) = 0 Factor a trinomial. 7((-1 + -3p)(7 + -5p)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -3p)' equal to zero and attempt to solve: Simplifying -1 + -3p = 0 Solving -1 + -3p = 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 + -3p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3p = 0 + 1 -3p = 0 + 1 Combine like terms: 0 + 1 = 1 -3p = 1 Divide each side by '-3'. p = -0.3333333333 Simplifying p = -0.3333333333Subproblem 2
Set the factor '(7 + -5p)' equal to zero and attempt to solve: Simplifying 7 + -5p = 0 Solving 7 + -5p = 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 + -5p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5p = 0 + -7 -5p = 0 + -7 Combine like terms: 0 + -7 = -7 -5p = -7 Divide each side by '-5'. p = 1.4 Simplifying p = 1.4Solution
p = {-0.3333333333, 1.4}
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