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Simplifying 2p2 + 20p + -16 = 0 Reorder the terms: -16 + 20p + 2p2 = 0 Solving -16 + 20p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 10p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 10p + p2)' equal to zero and attempt to solve: Simplifying -8 + 10p + p2 = 0 Solving -8 + 10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 10p + 8 + p2 = 0 + 8 Reorder the terms: -8 + 8 + 10p + p2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 10p + p2 = 0 + 8 10p + p2 = 0 + 8 Combine like terms: 0 + 8 = 8 10p + p2 = 8 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 8 + 25 Reorder the terms: 25 + 10p + p2 = 8 + 25 Combine like terms: 8 + 25 = 33 25 + 10p + p2 = 33 Factor a perfect square on the left side: (p + 5)(p + 5) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (p + 5) equal to 5.744562647 and -5.744562647.Subproblem 1
p + 5 = 5.744562647 Simplifying p + 5 = 5.744562647 Reorder the terms: 5 + p = 5.744562647 Solving 5 + p = 5.744562647 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 5.744562647 + -5 Combine like terms: 5 + -5 = 0 0 + p = 5.744562647 + -5 p = 5.744562647 + -5 Combine like terms: 5.744562647 + -5 = 0.744562647 p = 0.744562647 Simplifying p = 0.744562647Subproblem 2
p + 5 = -5.744562647 Simplifying p + 5 = -5.744562647 Reorder the terms: 5 + p = -5.744562647 Solving 5 + p = -5.744562647 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -5.744562647 + -5 Combine like terms: 5 + -5 = 0 0 + p = -5.744562647 + -5 p = -5.744562647 + -5 Combine like terms: -5.744562647 + -5 = -10.744562647 p = -10.744562647 Simplifying p = -10.744562647Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.744562647, -10.744562647}Solution
p = {0.744562647, -10.744562647}
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