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Simplifying 3.15p2 + -5.89p = 2.63 Reorder the terms: -5.89p + 3.15p2 = 2.63 Solving -5.89p + 3.15p2 = 2.63 Solving for variable 'p'. Reorder the terms: -2.63 + -5.89p + 3.15p2 = 2.63 + -2.63 Combine like terms: 2.63 + -2.63 = 0.00 -2.63 + -5.89p + 3.15p2 = 0.00 Begin completing the square. Divide all terms by 3.15 the coefficient of the squared term: Divide each side by '3.15'. -0.8349206349 + -1.86984127p + p2 = 0 Move the constant term to the right: Add '0.8349206349' to each side of the equation. -0.8349206349 + -1.86984127p + 0.8349206349 + p2 = 0 + 0.8349206349 Reorder the terms: -0.8349206349 + 0.8349206349 + -1.86984127p + p2 = 0 + 0.8349206349 Combine like terms: -0.8349206349 + 0.8349206349 = 0.0000000000 0.0000000000 + -1.86984127p + p2 = 0 + 0.8349206349 -1.86984127p + p2 = 0 + 0.8349206349 Combine like terms: 0 + 0.8349206349 = 0.8349206349 -1.86984127p + p2 = 0.8349206349 The p term is -1.86984127p. Take half its coefficient (-0.934920635). Square it (0.8740765937) and add it to both sides. Add '0.8740765937' to each side of the equation. -1.86984127p + 0.8740765937 + p2 = 0.8349206349 + 0.8740765937 Reorder the terms: 0.8740765937 + -1.86984127p + p2 = 0.8349206349 + 0.8740765937 Combine like terms: 0.8349206349 + 0.8740765937 = 1.7089972286 0.8740765937 + -1.86984127p + p2 = 1.7089972286 Factor a perfect square on the left side: (p + -0.934920635)(p + -0.934920635) = 1.7089972286 Calculate the square root of the right side: 1.307286208 Break this problem into two subproblems by setting (p + -0.934920635) equal to 1.307286208 and -1.307286208.Subproblem 1
p + -0.934920635 = 1.307286208 Simplifying p + -0.934920635 = 1.307286208 Reorder the terms: -0.934920635 + p = 1.307286208 Solving -0.934920635 + p = 1.307286208 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.934920635' to each side of the equation. -0.934920635 + 0.934920635 + p = 1.307286208 + 0.934920635 Combine like terms: -0.934920635 + 0.934920635 = 0.000000000 0.000000000 + p = 1.307286208 + 0.934920635 p = 1.307286208 + 0.934920635 Combine like terms: 1.307286208 + 0.934920635 = 2.242206843 p = 2.242206843 Simplifying p = 2.242206843Subproblem 2
p + -0.934920635 = -1.307286208 Simplifying p + -0.934920635 = -1.307286208 Reorder the terms: -0.934920635 + p = -1.307286208 Solving -0.934920635 + p = -1.307286208 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.934920635' to each side of the equation. -0.934920635 + 0.934920635 + p = -1.307286208 + 0.934920635 Combine like terms: -0.934920635 + 0.934920635 = 0.000000000 0.000000000 + p = -1.307286208 + 0.934920635 p = -1.307286208 + 0.934920635 Combine like terms: -1.307286208 + 0.934920635 = -0.372365573 p = -0.372365573 Simplifying p = -0.372365573Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.242206843, -0.372365573}
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