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Simplifying 3p2 + -52p + 168 = 0 Reorder the terms: 168 + -52p + 3p2 = 0 Solving 168 + -52p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 56 + -17.33333333p + p2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + -17.33333333p + -56 + p2 = 0 + -56 Reorder the terms: 56 + -56 + -17.33333333p + p2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -17.33333333p + p2 = 0 + -56 -17.33333333p + p2 = 0 + -56 Combine like terms: 0 + -56 = -56 -17.33333333p + p2 = -56 The p term is -17.33333333p. Take half its coefficient (-8.666666665). Square it (75.11111108) and add it to both sides. Add '75.11111108' to each side of the equation. -17.33333333p + 75.11111108 + p2 = -56 + 75.11111108 Reorder the terms: 75.11111108 + -17.33333333p + p2 = -56 + 75.11111108 Combine like terms: -56 + 75.11111108 = 19.11111108 75.11111108 + -17.33333333p + p2 = 19.11111108 Factor a perfect square on the left side: (p + -8.666666665)(p + -8.666666665) = 19.11111108 Calculate the square root of the right side: 4.371625679 Break this problem into two subproblems by setting (p + -8.666666665) equal to 4.371625679 and -4.371625679.Subproblem 1
p + -8.666666665 = 4.371625679 Simplifying p + -8.666666665 = 4.371625679 Reorder the terms: -8.666666665 + p = 4.371625679 Solving -8.666666665 + p = 4.371625679 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + p = 4.371625679 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + p = 4.371625679 + 8.666666665 p = 4.371625679 + 8.666666665 Combine like terms: 4.371625679 + 8.666666665 = 13.038292344 p = 13.038292344 Simplifying p = 13.038292344Subproblem 2
p + -8.666666665 = -4.371625679 Simplifying p + -8.666666665 = -4.371625679 Reorder the terms: -8.666666665 + p = -4.371625679 Solving -8.666666665 + p = -4.371625679 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + p = -4.371625679 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + p = -4.371625679 + 8.666666665 p = -4.371625679 + 8.666666665 Combine like terms: -4.371625679 + 8.666666665 = 4.295040986 p = 4.295040986 Simplifying p = 4.295040986Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.038292344, 4.295040986}
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