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Simplifying -4p2 + 116p = 144 Reorder the terms: 116p + -4p2 = 144 Solving 116p + -4p2 = 144 Solving for variable 'p'. Reorder the terms: -144 + 116p + -4p2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 116p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + 29p + -1p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-36 + 29p + -1p2)' equal to zero and attempt to solve: Simplifying -36 + 29p + -1p2 = 0 Solving -36 + 29p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -29p + p2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -29p + -36 + p2 = 0 + -36 Reorder the terms: 36 + -36 + -29p + p2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -29p + p2 = 0 + -36 -29p + p2 = 0 + -36 Combine like terms: 0 + -36 = -36 -29p + p2 = -36 The p term is -29p. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29p + 210.25 + p2 = -36 + 210.25 Reorder the terms: 210.25 + -29p + p2 = -36 + 210.25 Combine like terms: -36 + 210.25 = 174.25 210.25 + -29p + p2 = 174.25 Factor a perfect square on the left side: (p + -14.5)(p + -14.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (p + -14.5) equal to 13.200378782 and -13.200378782.Subproblem 1
p + -14.5 = 13.200378782 Simplifying p + -14.5 = 13.200378782 Reorder the terms: -14.5 + p = 13.200378782 Solving -14.5 + p = 13.200378782 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + p = 13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + p = 13.200378782 + 14.5 p = 13.200378782 + 14.5 Combine like terms: 13.200378782 + 14.5 = 27.700378782 p = 27.700378782 Simplifying p = 27.700378782Subproblem 2
p + -14.5 = -13.200378782 Simplifying p + -14.5 = -13.200378782 Reorder the terms: -14.5 + p = -13.200378782 Solving -14.5 + p = -13.200378782 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + p = -13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + p = -13.200378782 + 14.5 p = -13.200378782 + 14.5 Combine like terms: -13.200378782 + 14.5 = 1.299621218 p = 1.299621218 Simplifying p = 1.299621218Solution
The solution to the problem is based on the solutions from the subproblems. p = {27.700378782, 1.299621218}Solution
p = {27.700378782, 1.299621218}
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