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Simplifying 4p2 + -32p = 60 Reorder the terms: -32p + 4p2 = 60 Solving -32p + 4p2 = 60 Solving for variable 'p'. Reorder the terms: -60 + -32p + 4p2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -32p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -8p + p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -8p + p2)' equal to zero and attempt to solve: Simplifying -15 + -8p + p2 = 0 Solving -15 + -8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -8p + 15 + p2 = 0 + 15 Reorder the terms: -15 + 15 + -8p + p2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8p + p2 = 0 + 15 -8p + p2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8p + p2 = 15 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = 15 + 16 Reorder the terms: 16 + -8p + p2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + -8p + p2 = 31 Factor a perfect square on the left side: (p + -4)(p + -4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (p + -4) equal to 5.567764363 and -5.567764363.Subproblem 1
p + -4 = 5.567764363 Simplifying p + -4 = 5.567764363 Reorder the terms: -4 + p = 5.567764363 Solving -4 + p = 5.567764363 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + p = 5.567764363 + 4 p = 5.567764363 + 4 Combine like terms: 5.567764363 + 4 = 9.567764363 p = 9.567764363 Simplifying p = 9.567764363Subproblem 2
p + -4 = -5.567764363 Simplifying p + -4 = -5.567764363 Reorder the terms: -4 + p = -5.567764363 Solving -4 + p = -5.567764363 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + p = -5.567764363 + 4 p = -5.567764363 + 4 Combine like terms: -5.567764363 + 4 = -1.567764363 p = -1.567764363 Simplifying p = -1.567764363Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.567764363, -1.567764363}Solution
p = {9.567764363, -1.567764363}
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