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Simplifying p2 + -36p + 8 = 0 Reorder the terms: 8 + -36p + p2 = 0 Solving 8 + -36p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -36p + -8 + p2 = 0 + -8 Reorder the terms: 8 + -8 + -36p + p2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -36p + p2 = 0 + -8 -36p + p2 = 0 + -8 Combine like terms: 0 + -8 = -8 -36p + p2 = -8 The p term is -36p. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36p + 324 + p2 = -8 + 324 Reorder the terms: 324 + -36p + p2 = -8 + 324 Combine like terms: -8 + 324 = 316 324 + -36p + p2 = 316 Factor a perfect square on the left side: (p + -18)(p + -18) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (p + -18) equal to 17.776388835 and -17.776388835.Subproblem 1
p + -18 = 17.776388835 Simplifying p + -18 = 17.776388835 Reorder the terms: -18 + p = 17.776388835 Solving -18 + p = 17.776388835 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + p = 17.776388835 + 18 Combine like terms: -18 + 18 = 0 0 + p = 17.776388835 + 18 p = 17.776388835 + 18 Combine like terms: 17.776388835 + 18 = 35.776388835 p = 35.776388835 Simplifying p = 35.776388835Subproblem 2
p + -18 = -17.776388835 Simplifying p + -18 = -17.776388835 Reorder the terms: -18 + p = -17.776388835 Solving -18 + p = -17.776388835 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + p = -17.776388835 + 18 Combine like terms: -18 + 18 = 0 0 + p = -17.776388835 + 18 p = -17.776388835 + 18 Combine like terms: -17.776388835 + 18 = 0.223611165 p = 0.223611165 Simplifying p = 0.223611165Solution
The solution to the problem is based on the solutions from the subproblems. p = {35.776388835, 0.223611165}
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