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Simplifying -2p2 + 8p + -4 = 0 Reorder the terms: -4 + 8p + -2p2 = 0 Solving -4 + 8p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 4p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 4p + -1p2)' equal to zero and attempt to solve: Simplifying -2 + 4p + -1p2 = 0 Solving -2 + 4p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -4p + p2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4p + -2 + p2 = 0 + -2 Reorder the terms: 2 + -2 + -4p + p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4p + p2 = 0 + -2 -4p + p2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4p + p2 = -2 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 = -2 + 4 Reorder the terms: 4 + -4p + p2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4p + p2 = 2 Factor a perfect square on the left side: (p + -2)(p + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (p + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
p + -2 = 1.414213562 Simplifying p + -2 = 1.414213562 Reorder the terms: -2 + p = 1.414213562 Solving -2 + p = 1.414213562 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 = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + p = 1.414213562 + 2 p = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 p = 3.414213562 Simplifying p = 3.414213562Subproblem 2
p + -2 = -1.414213562 Simplifying p + -2 = -1.414213562 Reorder the terms: -2 + p = -1.414213562 Solving -2 + p = -1.414213562 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 = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + p = -1.414213562 + 2 p = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 p = 0.585786438 Simplifying p = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.414213562, 0.585786438}Solution
p = {3.414213562, 0.585786438}
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