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Simplifying 9p2 + -18p + -88 = 0 Reorder the terms: -88 + -18p + 9p2 = 0 Solving -88 + -18p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -9.777777778 + -2p + p2 = 0 Move the constant term to the right: Add '9.777777778' to each side of the equation. -9.777777778 + -2p + 9.777777778 + p2 = 0 + 9.777777778 Reorder the terms: -9.777777778 + 9.777777778 + -2p + p2 = 0 + 9.777777778 Combine like terms: -9.777777778 + 9.777777778 = 0.000000000 0.000000000 + -2p + p2 = 0 + 9.777777778 -2p + p2 = 0 + 9.777777778 Combine like terms: 0 + 9.777777778 = 9.777777778 -2p + p2 = 9.777777778 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 9.777777778 + 1 Reorder the terms: 1 + -2p + p2 = 9.777777778 + 1 Combine like terms: 9.777777778 + 1 = 10.777777778 1 + -2p + p2 = 10.777777778 Factor a perfect square on the left side: (p + -1)(p + -1) = 10.777777778 Calculate the square root of the right side: 3.282952601 Break this problem into two subproblems by setting (p + -1) equal to 3.282952601 and -3.282952601.Subproblem 1
p + -1 = 3.282952601 Simplifying p + -1 = 3.282952601 Reorder the terms: -1 + p = 3.282952601 Solving -1 + p = 3.282952601 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 3.282952601 + 1 Combine like terms: -1 + 1 = 0 0 + p = 3.282952601 + 1 p = 3.282952601 + 1 Combine like terms: 3.282952601 + 1 = 4.282952601 p = 4.282952601 Simplifying p = 4.282952601Subproblem 2
p + -1 = -3.282952601 Simplifying p + -1 = -3.282952601 Reorder the terms: -1 + p = -3.282952601 Solving -1 + p = -3.282952601 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -3.282952601 + 1 Combine like terms: -1 + 1 = 0 0 + p = -3.282952601 + 1 p = -3.282952601 + 1 Combine like terms: -3.282952601 + 1 = -2.282952601 p = -2.282952601 Simplifying p = -2.282952601Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.282952601, -2.282952601}
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