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Simplifying 2p2 + 16p + -4 = 0 Reorder the terms: -4 + 16p + 2p2 = 0 Solving -4 + 16p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 8p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 8p + p2)' equal to zero and attempt to solve: Simplifying -2 + 8p + p2 = 0 Solving -2 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 8p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 8p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 8p + p2 = 0 + 2 8p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 8p + p2 = 2 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 2 + 16 Reorder the terms: 16 + 8p + p2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + 8p + p2 = 18 Factor a perfect square on the left side: (p + 4)(p + 4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (p + 4) equal to 4.242640687 and -4.242640687.Subproblem 1
p + 4 = 4.242640687 Simplifying p + 4 = 4.242640687 Reorder the terms: 4 + p = 4.242640687 Solving 4 + p = 4.242640687 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + p = 4.242640687 + -4 p = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 p = 0.242640687 Simplifying p = 0.242640687Subproblem 2
p + 4 = -4.242640687 Simplifying p + 4 = -4.242640687 Reorder the terms: 4 + p = -4.242640687 Solving 4 + p = -4.242640687 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + p = -4.242640687 + -4 p = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 p = -8.242640687 Simplifying p = -8.242640687Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.242640687, -8.242640687}Solution
p = {0.242640687, -8.242640687}
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