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Simplifying 2p2 + -7p + -17 = 0 Reorder the terms: -17 + -7p + 2p2 = 0 Solving -17 + -7p + 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'. -8.5 + -3.5p + p2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -3.5p + 8.5 + p2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -3.5p + p2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -3.5p + p2 = 0 + 8.5 -3.5p + p2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -3.5p + p2 = 8.5 The p term is -3.5p. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5p + 3.0625 + p2 = 8.5 + 3.0625 Reorder the terms: 3.0625 + -3.5p + p2 = 8.5 + 3.0625 Combine like terms: 8.5 + 3.0625 = 11.5625 3.0625 + -3.5p + p2 = 11.5625 Factor a perfect square on the left side: (p + -1.75)(p + -1.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (p + -1.75) equal to 3.400367627 and -3.400367627.Subproblem 1
p + -1.75 = 3.400367627 Simplifying p + -1.75 = 3.400367627 Reorder the terms: -1.75 + p = 3.400367627 Solving -1.75 + p = 3.400367627 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = 3.400367627 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = 3.400367627 + 1.75 p = 3.400367627 + 1.75 Combine like terms: 3.400367627 + 1.75 = 5.150367627 p = 5.150367627 Simplifying p = 5.150367627Subproblem 2
p + -1.75 = -3.400367627 Simplifying p + -1.75 = -3.400367627 Reorder the terms: -1.75 + p = -3.400367627 Solving -1.75 + p = -3.400367627 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = -3.400367627 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = -3.400367627 + 1.75 p = -3.400367627 + 1.75 Combine like terms: -3.400367627 + 1.75 = -1.650367627 p = -1.650367627 Simplifying p = -1.650367627Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.150367627, -1.650367627}
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