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Simplifying 6p2 + -74p + 33 = -99 Reorder the terms: 33 + -74p + 6p2 = -99 Solving 33 + -74p + 6p2 = -99 Solving for variable 'p'. Reorder the terms: 33 + 99 + -74p + 6p2 = -99 + 99 Combine like terms: 33 + 99 = 132 132 + -74p + 6p2 = -99 + 99 Combine like terms: -99 + 99 = 0 132 + -74p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(66 + -37p + 3p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(66 + -37p + 3p2)' equal to zero and attempt to solve: Simplifying 66 + -37p + 3p2 = 0 Solving 66 + -37p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 22 + -12.33333333p + p2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -12.33333333p + -22 + p2 = 0 + -22 Reorder the terms: 22 + -22 + -12.33333333p + p2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -12.33333333p + p2 = 0 + -22 -12.33333333p + p2 = 0 + -22 Combine like terms: 0 + -22 = -22 -12.33333333p + p2 = -22 The p term is -12.33333333p. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333p + 38.02777776 + p2 = -22 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333p + p2 = -22 + 38.02777776 Combine like terms: -22 + 38.02777776 = 16.02777776 38.02777776 + -12.33333333p + p2 = 16.02777776 Factor a perfect square on the left side: (p + -6.166666665)(p + -6.166666665) = 16.02777776 Calculate the square root of the right side: 4.003470714 Break this problem into two subproblems by setting (p + -6.166666665) equal to 4.003470714 and -4.003470714.Subproblem 1
p + -6.166666665 = 4.003470714 Simplifying p + -6.166666665 = 4.003470714 Reorder the terms: -6.166666665 + p = 4.003470714 Solving -6.166666665 + p = 4.003470714 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + p = 4.003470714 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + p = 4.003470714 + 6.166666665 p = 4.003470714 + 6.166666665 Combine like terms: 4.003470714 + 6.166666665 = 10.170137379 p = 10.170137379 Simplifying p = 10.170137379Subproblem 2
p + -6.166666665 = -4.003470714 Simplifying p + -6.166666665 = -4.003470714 Reorder the terms: -6.166666665 + p = -4.003470714 Solving -6.166666665 + p = -4.003470714 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + p = -4.003470714 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + p = -4.003470714 + 6.166666665 p = -4.003470714 + 6.166666665 Combine like terms: -4.003470714 + 6.166666665 = 2.163195951 p = 2.163195951 Simplifying p = 2.163195951Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.170137379, 2.163195951}Solution
p = {10.170137379, 2.163195951}
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