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Simplifying -2p2 + -30p + 4 = 0 Reorder the terms: 4 + -30p + -2p2 = 0 Solving 4 + -30p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -15p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -15p + -1p2)' equal to zero and attempt to solve: Simplifying 2 + -15p + -1p2 = 0 Solving 2 + -15p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 15p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 15p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 15p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 15p + p2 = 0 + 2 15p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 15p + p2 = 2 The p term is 15p. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15p + 56.25 + p2 = 2 + 56.25 Reorder the terms: 56.25 + 15p + p2 = 2 + 56.25 Combine like terms: 2 + 56.25 = 58.25 56.25 + 15p + p2 = 58.25 Factor a perfect square on the left side: (p + 7.5)(p + 7.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (p + 7.5) equal to 7.632168761 and -7.632168761.Subproblem 1
p + 7.5 = 7.632168761 Simplifying p + 7.5 = 7.632168761 Reorder the terms: 7.5 + p = 7.632168761 Solving 7.5 + p = 7.632168761 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + p = 7.632168761 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + p = 7.632168761 + -7.5 p = 7.632168761 + -7.5 Combine like terms: 7.632168761 + -7.5 = 0.132168761 p = 0.132168761 Simplifying p = 0.132168761Subproblem 2
p + 7.5 = -7.632168761 Simplifying p + 7.5 = -7.632168761 Reorder the terms: 7.5 + p = -7.632168761 Solving 7.5 + p = -7.632168761 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + p = -7.632168761 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + p = -7.632168761 + -7.5 p = -7.632168761 + -7.5 Combine like terms: -7.632168761 + -7.5 = -15.132168761 p = -15.132168761 Simplifying p = -15.132168761Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.132168761, -15.132168761}Solution
p = {0.132168761, -15.132168761}
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