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Simplifying 9p2 = 12p + 4 Reorder the terms: 9p2 = 4 + 12p Solving 9p2 = 4 + 12p Solving for variable 'p'. Reorder the terms: -4 + -12p + 9p2 = 4 + 12p + -4 + -12p Reorder the terms: -4 + -12p + 9p2 = 4 + -4 + 12p + -12p Combine like terms: 4 + -4 = 0 -4 + -12p + 9p2 = 0 + 12p + -12p -4 + -12p + 9p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -4 + -12p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -1.333333333p + p2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.333333333p + 0.4444444444 + p2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.333333333p + p2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.333333333p + p2 = 0 + 0.4444444444 -1.333333333p + p2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.333333333p + p2 = 0.4444444444 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 = 0.4444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333p + p2 = 0.4444444444 + 0.4444444442 Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886 0.4444444442 + -1.333333333p + p2 = 0.8888888886 Factor a perfect square on the left side: (p + -0.6666666665)(p + -0.6666666665) = 0.8888888886 Calculate the square root of the right side: 0.942809041 Break this problem into two subproblems by setting (p + -0.6666666665) equal to 0.942809041 and -0.942809041.Subproblem 1
p + -0.6666666665 = 0.942809041 Simplifying p + -0.6666666665 = 0.942809041 Reorder the terms: -0.6666666665 + p = 0.942809041 Solving -0.6666666665 + p = 0.942809041 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 = 0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + p = 0.942809041 + 0.6666666665 p = 0.942809041 + 0.6666666665 Combine like terms: 0.942809041 + 0.6666666665 = 1.6094757075 p = 1.6094757075 Simplifying p = 1.6094757075Subproblem 2
p + -0.6666666665 = -0.942809041 Simplifying p + -0.6666666665 = -0.942809041 Reorder the terms: -0.6666666665 + p = -0.942809041 Solving -0.6666666665 + p = -0.942809041 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 = -0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + p = -0.942809041 + 0.6666666665 p = -0.942809041 + 0.6666666665 Combine like terms: -0.942809041 + 0.6666666665 = -0.2761423745 p = -0.2761423745 Simplifying p = -0.2761423745Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.6094757075, -0.2761423745}
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