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Simplifying 9p2 + -8p + -9 = 0 Reorder the terms: -9 + -8p + 9p2 = 0 Solving -9 + -8p + 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'. -1 + -0.8888888889p + p2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8888888889p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8888888889p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8888888889p + p2 = 0 + 1 -0.8888888889p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8888888889p + p2 = 1 The p term is -0.8888888889p. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889p + 0.1975308642 + p2 = 1 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889p + p2 = 1 + 0.1975308642 Combine like terms: 1 + 0.1975308642 = 1.1975308642 0.1975308642 + -0.8888888889p + p2 = 1.1975308642 Factor a perfect square on the left side: (p + -0.4444444445)(p + -0.4444444445) = 1.1975308642 Calculate the square root of the right side: 1.094317534 Break this problem into two subproblems by setting (p + -0.4444444445) equal to 1.094317534 and -1.094317534.Subproblem 1
p + -0.4444444445 = 1.094317534 Simplifying p + -0.4444444445 = 1.094317534 Reorder the terms: -0.4444444445 + p = 1.094317534 Solving -0.4444444445 + p = 1.094317534 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + p = 1.094317534 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + p = 1.094317534 + 0.4444444445 p = 1.094317534 + 0.4444444445 Combine like terms: 1.094317534 + 0.4444444445 = 1.5387619785 p = 1.5387619785 Simplifying p = 1.5387619785Subproblem 2
p + -0.4444444445 = -1.094317534 Simplifying p + -0.4444444445 = -1.094317534 Reorder the terms: -0.4444444445 + p = -1.094317534 Solving -0.4444444445 + p = -1.094317534 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + p = -1.094317534 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + p = -1.094317534 + 0.4444444445 p = -1.094317534 + 0.4444444445 Combine like terms: -1.094317534 + 0.4444444445 = -0.6498730895 p = -0.6498730895 Simplifying p = -0.6498730895Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.5387619785, -0.6498730895}
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