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Simplifying 9p^{2}+ 18p = 10 Reorder the terms: 18p + 9p^{2}= 10 Solving 18p + 9p^{2}= 10 Solving for variable 'p'. Reorder the terms: -10 + 18p + 9p^{2}= 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 18p + 9p^{2}= 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 2p + p^{2}= 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 2p + 1.111111111 + p^{2}= 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 2p + p^{2}= 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 2p + p^{2}= 0 + 1.111111111 2p + p^{2}= 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 2p + p^{2}= 1.111111111 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 + p^{2}= 1.111111111 + 1 Reorder the terms: 1 + 2p + p^{2}= 1.111111111 + 1 Combine like terms: 1.111111111 + 1 = 2.111111111 1 + 2p + p^{2}= 2.111111111 Factor a perfect square on the left side: (p + 1)(p + 1) = 2.111111111 Calculate the square root of the right side: 1.452966314 Break this problem into two subproblems by setting (p + 1) equal to 1.452966314 and -1.452966314.## Subproblem 1

p + 1 = 1.452966314 Simplifying p + 1 = 1.452966314 Reorder the terms: 1 + p = 1.452966314 Solving 1 + p = 1.452966314 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 = 1.452966314 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.452966314 + -1 p = 1.452966314 + -1 Combine like terms: 1.452966314 + -1 = 0.452966314 p = 0.452966314 Simplifying p = 0.452966314## Subproblem 2

p + 1 = -1.452966314 Simplifying p + 1 = -1.452966314 Reorder the terms: 1 + p = -1.452966314 Solving 1 + p = -1.452966314 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 = -1.452966314 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.452966314 + -1 p = -1.452966314 + -1 Combine like terms: -1.452966314 + -1 = -2.452966314 p = -2.452966314 Simplifying p = -2.452966314## Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.452966314, -2.452966314}

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