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Simplifying 10p2 + 60p = 50 Reorder the terms: 60p + 10p2 = 50 Solving 60p + 10p2 = 50 Solving for variable 'p'. Reorder the terms: -50 + 60p + 10p2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 60p + 10p2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-5 + 6p + p2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-5 + 6p + p2)' equal to zero and attempt to solve: Simplifying -5 + 6p + p2 = 0 Solving -5 + 6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 6p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + 6p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6p + p2 = 0 + 5 6p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 6p + p2 = 5 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 5 + 9 Reorder the terms: 9 + 6p + p2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6p + p2 = 14 Factor a perfect square on the left side: (p + 3)(p + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (p + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
p + 3 = 3.741657387 Simplifying p + 3 = 3.741657387 Reorder the terms: 3 + p = 3.741657387 Solving 3 + p = 3.741657387 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.741657387 + -3 p = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 p = 0.741657387 Simplifying p = 0.741657387Subproblem 2
p + 3 = -3.741657387 Simplifying p + 3 = -3.741657387 Reorder the terms: 3 + p = -3.741657387 Solving 3 + p = -3.741657387 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.741657387 + -3 p = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 p = -6.741657387 Simplifying p = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.741657387, -6.741657387}Solution
p = {0.741657387, -6.741657387}
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