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Simplifying -2p2 + -8p + 50 = 0 Reorder the terms: 50 + -8p + -2p2 = 0 Solving 50 + -8p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -4p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -4p + -1p2)' equal to zero and attempt to solve: Simplifying 25 + -4p + -1p2 = 0 Solving 25 + -4p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 4p + p2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 4p + 25 + p2 = 0 + 25 Reorder the terms: -25 + 25 + 4p + p2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4p + p2 = 0 + 25 4p + p2 = 0 + 25 Combine like terms: 0 + 25 = 25 4p + p2 = 25 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 25 + 4 Reorder the terms: 4 + 4p + p2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + 4p + p2 = 29 Factor a perfect square on the left side: (p + 2)(p + 2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (p + 2) equal to 5.385164807 and -5.385164807.Subproblem 1
p + 2 = 5.385164807 Simplifying p + 2 = 5.385164807 Reorder the terms: 2 + p = 5.385164807 Solving 2 + p = 5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + p = 5.385164807 + -2 p = 5.385164807 + -2 Combine like terms: 5.385164807 + -2 = 3.385164807 p = 3.385164807 Simplifying p = 3.385164807Subproblem 2
p + 2 = -5.385164807 Simplifying p + 2 = -5.385164807 Reorder the terms: 2 + p = -5.385164807 Solving 2 + p = -5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + p = -5.385164807 + -2 p = -5.385164807 + -2 Combine like terms: -5.385164807 + -2 = -7.385164807 p = -7.385164807 Simplifying p = -7.385164807Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.385164807, -7.385164807}Solution
p = {3.385164807, -7.385164807}
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