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Simplifying 2p2 + -18p + 23 = 0 Reorder the terms: 23 + -18p + 2p2 = 0 Solving 23 + -18p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + -9p + p2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -9p + -11.5 + p2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -9p + p2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -9p + p2 = 0 + -11.5 -9p + p2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -9p + p2 = -11.5 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = -11.5 + 20.25 Reorder the terms: 20.25 + -9p + p2 = -11.5 + 20.25 Combine like terms: -11.5 + 20.25 = 8.75 20.25 + -9p + p2 = 8.75 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (p + -4.5) equal to 2.958039892 and -2.958039892.Subproblem 1
p + -4.5 = 2.958039892 Simplifying p + -4.5 = 2.958039892 Reorder the terms: -4.5 + p = 2.958039892 Solving -4.5 + p = 2.958039892 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 2.958039892 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 2.958039892 + 4.5 p = 2.958039892 + 4.5 Combine like terms: 2.958039892 + 4.5 = 7.458039892 p = 7.458039892 Simplifying p = 7.458039892Subproblem 2
p + -4.5 = -2.958039892 Simplifying p + -4.5 = -2.958039892 Reorder the terms: -4.5 + p = -2.958039892 Solving -4.5 + p = -2.958039892 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -2.958039892 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -2.958039892 + 4.5 p = -2.958039892 + 4.5 Combine like terms: -2.958039892 + 4.5 = 1.541960108 p = 1.541960108 Simplifying p = 1.541960108Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.458039892, 1.541960108}
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