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Simplifying 8p2 + 12p + -1 = 0 Reorder the terms: -1 + 12p + 8p2 = 0 Solving -1 + 12p + 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'. -0.125 + 1.5p + p2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 1.5p + 0.125 + p2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 1.5p + p2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 1.5p + p2 = 0 + 0.125 1.5p + p2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 1.5p + p2 = 0.125 The p term is 1.5p. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5p + 0.5625 + p2 = 0.125 + 0.5625 Reorder the terms: 0.5625 + 1.5p + p2 = 0.125 + 0.5625 Combine like terms: 0.125 + 0.5625 = 0.6875 0.5625 + 1.5p + p2 = 0.6875 Factor a perfect square on the left side: (p + 0.75)(p + 0.75) = 0.6875 Calculate the square root of the right side: 0.829156198 Break this problem into two subproblems by setting (p + 0.75) equal to 0.829156198 and -0.829156198.Subproblem 1
p + 0.75 = 0.829156198 Simplifying p + 0.75 = 0.829156198 Reorder the terms: 0.75 + p = 0.829156198 Solving 0.75 + p = 0.829156198 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = 0.829156198 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = 0.829156198 + -0.75 p = 0.829156198 + -0.75 Combine like terms: 0.829156198 + -0.75 = 0.079156198 p = 0.079156198 Simplifying p = 0.079156198Subproblem 2
p + 0.75 = -0.829156198 Simplifying p + 0.75 = -0.829156198 Reorder the terms: 0.75 + p = -0.829156198 Solving 0.75 + p = -0.829156198 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = -0.829156198 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = -0.829156198 + -0.75 p = -0.829156198 + -0.75 Combine like terms: -0.829156198 + -0.75 = -1.579156198 p = -1.579156198 Simplifying p = -1.579156198Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.079156198, -1.579156198}
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