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Simplifying 2p2 + 17 = 16p Reorder the terms: 17 + 2p2 = 16p Solving 17 + 2p2 = 16p Solving for variable 'p'. Reorder the terms: 17 + -16p + 2p2 = 16p + -16p Combine like terms: 16p + -16p = 0 17 + -16p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -8p + p2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -8p + -8.5 + p2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -8p + p2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -8p + p2 = 0 + -8.5 -8p + p2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -8p + p2 = -8.5 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = -8.5 + 16 Reorder the terms: 16 + -8p + p2 = -8.5 + 16 Combine like terms: -8.5 + 16 = 7.5 16 + -8p + p2 = 7.5 Factor a perfect square on the left side: (p + -4)(p + -4) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (p + -4) equal to 2.738612788 and -2.738612788.Subproblem 1
p + -4 = 2.738612788 Simplifying p + -4 = 2.738612788 Reorder the terms: -4 + p = 2.738612788 Solving -4 + p = 2.738612788 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 2.738612788 + 4 Combine like terms: -4 + 4 = 0 0 + p = 2.738612788 + 4 p = 2.738612788 + 4 Combine like terms: 2.738612788 + 4 = 6.738612788 p = 6.738612788 Simplifying p = 6.738612788Subproblem 2
p + -4 = -2.738612788 Simplifying p + -4 = -2.738612788 Reorder the terms: -4 + p = -2.738612788 Solving -4 + p = -2.738612788 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -2.738612788 + 4 Combine like terms: -4 + 4 = 0 0 + p = -2.738612788 + 4 p = -2.738612788 + 4 Combine like terms: -2.738612788 + 4 = 1.261387212 p = 1.261387212 Simplifying p = 1.261387212Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.738612788, 1.261387212}
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