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Simplifying 2p2 + -17p + 13 = 0 Reorder the terms: 13 + -17p + 2p2 = 0 Solving 13 + -17p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -8.5p + p2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -8.5p + -6.5 + p2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -8.5p + p2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -8.5p + p2 = 0 + -6.5 -8.5p + p2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -8.5p + p2 = -6.5 The p term is -8.5p. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5p + 18.0625 + p2 = -6.5 + 18.0625 Reorder the terms: 18.0625 + -8.5p + p2 = -6.5 + 18.0625 Combine like terms: -6.5 + 18.0625 = 11.5625 18.0625 + -8.5p + p2 = 11.5625 Factor a perfect square on the left side: (p + -4.25)(p + -4.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (p + -4.25) equal to 3.400367627 and -3.400367627.Subproblem 1
p + -4.25 = 3.400367627 Simplifying p + -4.25 = 3.400367627 Reorder the terms: -4.25 + p = 3.400367627 Solving -4.25 + p = 3.400367627 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + p = 3.400367627 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + p = 3.400367627 + 4.25 p = 3.400367627 + 4.25 Combine like terms: 3.400367627 + 4.25 = 7.650367627 p = 7.650367627 Simplifying p = 7.650367627Subproblem 2
p + -4.25 = -3.400367627 Simplifying p + -4.25 = -3.400367627 Reorder the terms: -4.25 + p = -3.400367627 Solving -4.25 + p = -3.400367627 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + p = -3.400367627 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + p = -3.400367627 + 4.25 p = -3.400367627 + 4.25 Combine like terms: -3.400367627 + 4.25 = 0.849632373 p = 0.849632373 Simplifying p = 0.849632373Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.650367627, 0.849632373}
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