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Simplifying 15 + -45p + 10p2 = 0 Solving 15 + -45p + 10p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -9p + 2p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -9p + 2p2)' equal to zero and attempt to solve: Simplifying 3 + -9p + 2p2 = 0 Solving 3 + -9p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -4.5p + p2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4.5p + -1.5 + p2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4.5p + p2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4.5p + p2 = 0 + -1.5 -4.5p + p2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4.5p + p2 = -1.5 The p term is -4.5p. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5p + 5.0625 + p2 = -1.5 + 5.0625 Reorder the terms: 5.0625 + -4.5p + p2 = -1.5 + 5.0625 Combine like terms: -1.5 + 5.0625 = 3.5625 5.0625 + -4.5p + p2 = 3.5625 Factor a perfect square on the left side: (p + -2.25)(p + -2.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (p + -2.25) equal to 1.887458609 and -1.887458609.Subproblem 1
p + -2.25 = 1.887458609 Simplifying p + -2.25 = 1.887458609 Reorder the terms: -2.25 + p = 1.887458609 Solving -2.25 + p = 1.887458609 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = 1.887458609 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = 1.887458609 + 2.25 p = 1.887458609 + 2.25 Combine like terms: 1.887458609 + 2.25 = 4.137458609 p = 4.137458609 Simplifying p = 4.137458609Subproblem 2
p + -2.25 = -1.887458609 Simplifying p + -2.25 = -1.887458609 Reorder the terms: -2.25 + p = -1.887458609 Solving -2.25 + p = -1.887458609 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = -1.887458609 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = -1.887458609 + 2.25 p = -1.887458609 + 2.25 Combine like terms: -1.887458609 + 2.25 = 0.362541391 p = 0.362541391 Simplifying p = 0.362541391Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.137458609, 0.362541391}Solution
p = {4.137458609, 0.362541391}
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