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Simplifying 9p2 + 18p + -20 = 0 Reorder the terms: -20 + 18p + 9p2 = 0 Solving -20 + 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'. -2.222222222 + 2p + p2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 2p + 2.222222222 + p2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 2p + p2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 2p + p2 = 0 + 2.222222222 2p + p2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 2p + p2 = 2.222222222 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 = 2.222222222 + 1 Reorder the terms: 1 + 2p + p2 = 2.222222222 + 1 Combine like terms: 2.222222222 + 1 = 3.222222222 1 + 2p + p2 = 3.222222222 Factor a perfect square on the left side: (p + 1)(p + 1) = 3.222222222 Calculate the square root of the right side: 1.795054936 Break this problem into two subproblems by setting (p + 1) equal to 1.795054936 and -1.795054936.Subproblem 1
p + 1 = 1.795054936 Simplifying p + 1 = 1.795054936 Reorder the terms: 1 + p = 1.795054936 Solving 1 + p = 1.795054936 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 = 1.795054936 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.795054936 + -1 p = 1.795054936 + -1 Combine like terms: 1.795054936 + -1 = 0.795054936 p = 0.795054936 Simplifying p = 0.795054936Subproblem 2
p + 1 = -1.795054936 Simplifying p + 1 = -1.795054936 Reorder the terms: 1 + p = -1.795054936 Solving 1 + p = -1.795054936 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 = -1.795054936 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.795054936 + -1 p = -1.795054936 + -1 Combine like terms: -1.795054936 + -1 = -2.795054936 p = -2.795054936 Simplifying p = -2.795054936Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.795054936, -2.795054936}
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