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Simplifying 0 = 5p2 + 240p + -160 Reorder the terms: 0 = -160 + 240p + 5p2 Solving 0 = -160 + 240p + 5p2 Solving for variable 'p'. Combine like terms: 0 + 160 = 160 160 + -240p + -5p2 = -160 + 240p + 5p2 + 160 + -240p + -5p2 Reorder the terms: 160 + -240p + -5p2 = -160 + 160 + 240p + -240p + 5p2 + -5p2 Combine like terms: -160 + 160 = 0 160 + -240p + -5p2 = 0 + 240p + -240p + 5p2 + -5p2 160 + -240p + -5p2 = 240p + -240p + 5p2 + -5p2 Combine like terms: 240p + -240p = 0 160 + -240p + -5p2 = 0 + 5p2 + -5p2 160 + -240p + -5p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 160 + -240p + -5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(32 + -48p + -1p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(32 + -48p + -1p2)' equal to zero and attempt to solve: Simplifying 32 + -48p + -1p2 = 0 Solving 32 + -48p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + 48p + p2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 48p + 32 + p2 = 0 + 32 Reorder the terms: -32 + 32 + 48p + p2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 48p + p2 = 0 + 32 48p + p2 = 0 + 32 Combine like terms: 0 + 32 = 32 48p + p2 = 32 The p term is 48p. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48p + 576 + p2 = 32 + 576 Reorder the terms: 576 + 48p + p2 = 32 + 576 Combine like terms: 32 + 576 = 608 576 + 48p + p2 = 608 Factor a perfect square on the left side: (p + 24)(p + 24) = 608 Calculate the square root of the right side: 24.657656012 Break this problem into two subproblems by setting (p + 24) equal to 24.657656012 and -24.657656012.Subproblem 1
p + 24 = 24.657656012 Simplifying p + 24 = 24.657656012 Reorder the terms: 24 + p = 24.657656012 Solving 24 + p = 24.657656012 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + p = 24.657656012 + -24 Combine like terms: 24 + -24 = 0 0 + p = 24.657656012 + -24 p = 24.657656012 + -24 Combine like terms: 24.657656012 + -24 = 0.657656012 p = 0.657656012 Simplifying p = 0.657656012Subproblem 2
p + 24 = -24.657656012 Simplifying p + 24 = -24.657656012 Reorder the terms: 24 + p = -24.657656012 Solving 24 + p = -24.657656012 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + p = -24.657656012 + -24 Combine like terms: 24 + -24 = 0 0 + p = -24.657656012 + -24 p = -24.657656012 + -24 Combine like terms: -24.657656012 + -24 = -48.657656012 p = -48.657656012 Simplifying p = -48.657656012Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.657656012, -48.657656012}Solution
p = {0.657656012, -48.657656012}
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