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Simplifying 6p2 + -8p = 3 Reorder the terms: -8p + 6p2 = 3 Solving -8p + 6p2 = 3 Solving for variable 'p'. Reorder the terms: -3 + -8p + 6p2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8p + 6p2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -1.333333333p + p2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.333333333p + 0.5 + p2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.333333333p + p2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.333333333p + p2 = 0 + 0.5 -1.333333333p + p2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.333333333p + p2 = 0.5 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 = 0.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333p + p2 = 0.5 + 0.4444444442 Combine like terms: 0.5 + 0.4444444442 = 0.9444444442 0.4444444442 + -1.333333333p + p2 = 0.9444444442 Factor a perfect square on the left side: (p + -0.6666666665)(p + -0.6666666665) = 0.9444444442 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (p + -0.6666666665) equal to 0.971825316 and -0.971825316.Subproblem 1
p + -0.6666666665 = 0.971825316 Simplifying p + -0.6666666665 = 0.971825316 Reorder the terms: -0.6666666665 + p = 0.971825316 Solving -0.6666666665 + p = 0.971825316 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 = 0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + p = 0.971825316 + 0.6666666665 p = 0.971825316 + 0.6666666665 Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825 p = 1.6384919825 Simplifying p = 1.6384919825Subproblem 2
p + -0.6666666665 = -0.971825316 Simplifying p + -0.6666666665 = -0.971825316 Reorder the terms: -0.6666666665 + p = -0.971825316 Solving -0.6666666665 + p = -0.971825316 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 = -0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + p = -0.971825316 + 0.6666666665 p = -0.971825316 + 0.6666666665 Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495 p = -0.3051586495 Simplifying p = -0.3051586495Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.6384919825, -0.3051586495}
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