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Simplifying 6p2 = 36p + 30 Reorder the terms: 6p2 = 30 + 36p Solving 6p2 = 30 + 36p Solving for variable 'p'. Reorder the terms: -30 + -36p + 6p2 = 30 + 36p + -30 + -36p Reorder the terms: -30 + -36p + 6p2 = 30 + -30 + 36p + -36p Combine like terms: 30 + -30 = 0 -30 + -36p + 6p2 = 0 + 36p + -36p -30 + -36p + 6p2 = 36p + -36p Combine like terms: 36p + -36p = 0 -30 + -36p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + -6p + p2) = 0 Ignore the factor 6.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 = 6.741657387 p = 6.741657387 Simplifying p = 6.741657387Subproblem 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 = -0.741657387 p = -0.741657387 Simplifying p = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.741657387, -0.741657387}Solution
p = {6.741657387, -0.741657387}
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