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Simplifying 0 = p2 + 36p + 8 Reorder the terms: 0 = 8 + 36p + p2 Solving 0 = 8 + 36p + p2 Solving for variable 'p'. Combine like terms: 0 + -8 = -8 -8 + -36p + -1p2 = 8 + 36p + p2 + -8 + -36p + -1p2 Reorder the terms: -8 + -36p + -1p2 = 8 + -8 + 36p + -36p + p2 + -1p2 Combine like terms: 8 + -8 = 0 -8 + -36p + -1p2 = 0 + 36p + -36p + p2 + -1p2 -8 + -36p + -1p2 = 36p + -36p + p2 + -1p2 Combine like terms: 36p + -36p = 0 -8 + -36p + -1p2 = 0 + p2 + -1p2 -8 + -36p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -8 + -36p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 36p + p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 36p + p2)' equal to zero and attempt to solve: Simplifying 8 + 36p + p2 = 0 Solving 8 + 36p + p2 = 0 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 = -0.223611165 p = -0.223611165 Simplifying p = -0.223611165Subproblem 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 = -35.776388835 p = -35.776388835 Simplifying p = -35.776388835Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.223611165, -35.776388835}Solution
p = {-0.223611165, -35.776388835}
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