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Simplifying -3p2 + 84p + -75 = 0 Reorder the terms: -75 + 84p + -3p2 = 0 Solving -75 + 84p + -3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 28p + -1p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + 28p + -1p2)' equal to zero and attempt to solve: Simplifying -25 + 28p + -1p2 = 0 Solving -25 + 28p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -28p + p2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -28p + -25 + p2 = 0 + -25 Reorder the terms: 25 + -25 + -28p + p2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -28p + p2 = 0 + -25 -28p + p2 = 0 + -25 Combine like terms: 0 + -25 = -25 -28p + p2 = -25 The p term is -28p. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28p + 196 + p2 = -25 + 196 Reorder the terms: 196 + -28p + p2 = -25 + 196 Combine like terms: -25 + 196 = 171 196 + -28p + p2 = 171 Factor a perfect square on the left side: (p + -14)(p + -14) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (p + -14) equal to 13.076696831 and -13.076696831.Subproblem 1
p + -14 = 13.076696831 Simplifying p + -14 = 13.076696831 Reorder the terms: -14 + p = 13.076696831 Solving -14 + p = 13.076696831 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + p = 13.076696831 + 14 Combine like terms: -14 + 14 = 0 0 + p = 13.076696831 + 14 p = 13.076696831 + 14 Combine like terms: 13.076696831 + 14 = 27.076696831 p = 27.076696831 Simplifying p = 27.076696831Subproblem 2
p + -14 = -13.076696831 Simplifying p + -14 = -13.076696831 Reorder the terms: -14 + p = -13.076696831 Solving -14 + p = -13.076696831 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + p = -13.076696831 + 14 Combine like terms: -14 + 14 = 0 0 + p = -13.076696831 + 14 p = -13.076696831 + 14 Combine like terms: -13.076696831 + 14 = 0.923303169 p = 0.923303169 Simplifying p = 0.923303169Solution
The solution to the problem is based on the solutions from the subproblems. p = {27.076696831, 0.923303169}Solution
p = {27.076696831, 0.923303169}
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