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Simplifying 9p2 + -12 = 4p Reorder the terms: -12 + 9p2 = 4p Solving -12 + 9p2 = 4p Solving for variable 'p'. Reorder the terms: -12 + -4p + 9p2 = 4p + -4p Combine like terms: 4p + -4p = 0 -12 + -4p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + -0.4444444444p + p2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.4444444444p + 1.333333333 + p2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.4444444444p + p2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.4444444444p + p2 = 0 + 1.333333333 -0.4444444444p + p2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.4444444444p + p2 = 1.333333333 The p term is -0.4444444444p. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444p + 0.04938271604 + p2 = 1.333333333 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444p + p2 = 1.333333333 + 0.04938271604 Combine like terms: 1.333333333 + 0.04938271604 = 1.38271604904 0.04938271604 + -0.4444444444p + p2 = 1.38271604904 Factor a perfect square on the left side: (p + -0.2222222222)(p + -0.2222222222) = 1.38271604904 Calculate the square root of the right side: 1.175889471 Break this problem into two subproblems by setting (p + -0.2222222222) equal to 1.175889471 and -1.175889471.Subproblem 1
p + -0.2222222222 = 1.175889471 Simplifying p + -0.2222222222 = 1.175889471 Reorder the terms: -0.2222222222 + p = 1.175889471 Solving -0.2222222222 + p = 1.175889471 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + p = 1.175889471 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + p = 1.175889471 + 0.2222222222 p = 1.175889471 + 0.2222222222 Combine like terms: 1.175889471 + 0.2222222222 = 1.3981116932 p = 1.3981116932 Simplifying p = 1.3981116932Subproblem 2
p + -0.2222222222 = -1.175889471 Simplifying p + -0.2222222222 = -1.175889471 Reorder the terms: -0.2222222222 + p = -1.175889471 Solving -0.2222222222 + p = -1.175889471 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + p = -1.175889471 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + p = -1.175889471 + 0.2222222222 p = -1.175889471 + 0.2222222222 Combine like terms: -1.175889471 + 0.2222222222 = -0.9536672488 p = -0.9536672488 Simplifying p = -0.9536672488Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.3981116932, -0.9536672488}
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