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Simplifying 9p2 + 12p + -77 = -4 Reorder the terms: -77 + 12p + 9p2 = -4 Solving -77 + 12p + 9p2 = -4 Solving for variable 'p'. Reorder the terms: -77 + 4 + 12p + 9p2 = -4 + 4 Combine like terms: -77 + 4 = -73 -73 + 12p + 9p2 = -4 + 4 Combine like terms: -4 + 4 = 0 -73 + 12p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.111111111 + 1.333333333p + p2 = 0 Move the constant term to the right: Add '8.111111111' to each side of the equation. -8.111111111 + 1.333333333p + 8.111111111 + p2 = 0 + 8.111111111 Reorder the terms: -8.111111111 + 8.111111111 + 1.333333333p + p2 = 0 + 8.111111111 Combine like terms: -8.111111111 + 8.111111111 = 0.000000000 0.000000000 + 1.333333333p + p2 = 0 + 8.111111111 1.333333333p + p2 = 0 + 8.111111111 Combine like terms: 0 + 8.111111111 = 8.111111111 1.333333333p + p2 = 8.111111111 The p term is 1.333333333p. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333p + 0.4444444442 + p2 = 8.111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333p + p2 = 8.111111111 + 0.4444444442 Combine like terms: 8.111111111 + 0.4444444442 = 8.5555555552 0.4444444442 + 1.333333333p + p2 = 8.5555555552 Factor a perfect square on the left side: (p + 0.6666666665)(p + 0.6666666665) = 8.5555555552 Calculate the square root of the right side: 2.924988129 Break this problem into two subproblems by setting (p + 0.6666666665) equal to 2.924988129 and -2.924988129.Subproblem 1
p + 0.6666666665 = 2.924988129 Simplifying p + 0.6666666665 = 2.924988129 Reorder the terms: 0.6666666665 + p = 2.924988129 Solving 0.6666666665 + p = 2.924988129 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + p = 2.924988129 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + p = 2.924988129 + -0.6666666665 p = 2.924988129 + -0.6666666665 Combine like terms: 2.924988129 + -0.6666666665 = 2.2583214625 p = 2.2583214625 Simplifying p = 2.2583214625Subproblem 2
p + 0.6666666665 = -2.924988129 Simplifying p + 0.6666666665 = -2.924988129 Reorder the terms: 0.6666666665 + p = -2.924988129 Solving 0.6666666665 + p = -2.924988129 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + p = -2.924988129 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + p = -2.924988129 + -0.6666666665 p = -2.924988129 + -0.6666666665 Combine like terms: -2.924988129 + -0.6666666665 = -3.5916547955 p = -3.5916547955 Simplifying p = -3.5916547955Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.2583214625, -3.5916547955}
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