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Simplifying -8p2 + 2p + 5 = 0 Reorder the terms: 5 + 2p + -8p2 = 0 Solving 5 + 2p + -8p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -0.25p + p2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.25p + 0.625 + p2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.25p + p2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.25p + p2 = 0 + 0.625 -0.25p + p2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.25p + p2 = 0.625 The p term is -0.25p. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25p + 0.015625 + p2 = 0.625 + 0.015625 Reorder the terms: 0.015625 + -0.25p + p2 = 0.625 + 0.015625 Combine like terms: 0.625 + 0.015625 = 0.640625 0.015625 + -0.25p + p2 = 0.640625 Factor a perfect square on the left side: (p + -0.125)(p + -0.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (p + -0.125) equal to 0.80039053 and -0.80039053.Subproblem 1
p + -0.125 = 0.80039053 Simplifying p + -0.125 = 0.80039053 Reorder the terms: -0.125 + p = 0.80039053 Solving -0.125 + p = 0.80039053 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + p = 0.80039053 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + p = 0.80039053 + 0.125 p = 0.80039053 + 0.125 Combine like terms: 0.80039053 + 0.125 = 0.92539053 p = 0.92539053 Simplifying p = 0.92539053Subproblem 2
p + -0.125 = -0.80039053 Simplifying p + -0.125 = -0.80039053 Reorder the terms: -0.125 + p = -0.80039053 Solving -0.125 + p = -0.80039053 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + p = -0.80039053 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + p = -0.80039053 + 0.125 p = -0.80039053 + 0.125 Combine like terms: -0.80039053 + 0.125 = -0.67539053 p = -0.67539053 Simplifying p = -0.67539053Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.92539053, -0.67539053}
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