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Simplifying 8p2 + -1p + -3 = 0 Reorder the terms: -3 + -1p + 8p2 = 0 Solving -3 + -1p + 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'. -0.375 + -0.125p + p2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.125p + 0.375 + p2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.125p + p2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.125p + p2 = 0 + 0.375 -0.125p + p2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.125p + p2 = 0.375 The p term is -0.125p. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125p + 0.00390625 + p2 = 0.375 + 0.00390625 Reorder the terms: 0.00390625 + -0.125p + p2 = 0.375 + 0.00390625 Combine like terms: 0.375 + 0.00390625 = 0.37890625 0.00390625 + -0.125p + p2 = 0.37890625 Factor a perfect square on the left side: (p + -0.0625)(p + -0.0625) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (p + -0.0625) equal to 0.615553613 and -0.615553613.Subproblem 1
p + -0.0625 = 0.615553613 Simplifying p + -0.0625 = 0.615553613 Reorder the terms: -0.0625 + p = 0.615553613 Solving -0.0625 + p = 0.615553613 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + p = 0.615553613 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + p = 0.615553613 + 0.0625 p = 0.615553613 + 0.0625 Combine like terms: 0.615553613 + 0.0625 = 0.678053613 p = 0.678053613 Simplifying p = 0.678053613Subproblem 2
p + -0.0625 = -0.615553613 Simplifying p + -0.0625 = -0.615553613 Reorder the terms: -0.0625 + p = -0.615553613 Solving -0.0625 + p = -0.615553613 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + p = -0.615553613 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + p = -0.615553613 + 0.0625 p = -0.615553613 + 0.0625 Combine like terms: -0.615553613 + 0.0625 = -0.553053613 p = -0.553053613 Simplifying p = -0.553053613Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.678053613, -0.553053613}
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