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Simplifying p2 + -10p = 31 Reorder the terms: -10p + p2 = 31 Solving -10p + p2 = 31 Solving for variable 'p'. Reorder the terms: -31 + -10p + p2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + -10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -10p + 31 + p2 = 0 + 31 Reorder the terms: -31 + 31 + -10p + p2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -10p + p2 = 0 + 31 -10p + p2 = 0 + 31 Combine like terms: 0 + 31 = 31 -10p + p2 = 31 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = 31 + 25 Reorder the terms: 25 + -10p + p2 = 31 + 25 Combine like terms: 31 + 25 = 56 25 + -10p + p2 = 56 Factor a perfect square on the left side: (p + -5)(p + -5) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (p + -5) equal to 7.483314774 and -7.483314774.Subproblem 1
p + -5 = 7.483314774 Simplifying p + -5 = 7.483314774 Reorder the terms: -5 + p = 7.483314774 Solving -5 + p = 7.483314774 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 7.483314774 + 5 Combine like terms: -5 + 5 = 0 0 + p = 7.483314774 + 5 p = 7.483314774 + 5 Combine like terms: 7.483314774 + 5 = 12.483314774 p = 12.483314774 Simplifying p = 12.483314774Subproblem 2
p + -5 = -7.483314774 Simplifying p + -5 = -7.483314774 Reorder the terms: -5 + p = -7.483314774 Solving -5 + p = -7.483314774 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -7.483314774 + 5 Combine like terms: -5 + 5 = 0 0 + p = -7.483314774 + 5 p = -7.483314774 + 5 Combine like terms: -7.483314774 + 5 = -2.483314774 p = -2.483314774 Simplifying p = -2.483314774Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.483314774, -2.483314774}
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