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Simplifying p2 + -18p + 66 = 0 Reorder the terms: 66 + -18p + p2 = 0 Solving 66 + -18p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-66' to each side of the equation. 66 + -18p + -66 + p2 = 0 + -66 Reorder the terms: 66 + -66 + -18p + p2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -18p + p2 = 0 + -66 -18p + p2 = 0 + -66 Combine like terms: 0 + -66 = -66 -18p + p2 = -66 The p term is -18p. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18p + 81 + p2 = -66 + 81 Reorder the terms: 81 + -18p + p2 = -66 + 81 Combine like terms: -66 + 81 = 15 81 + -18p + p2 = 15 Factor a perfect square on the left side: (p + -9)(p + -9) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (p + -9) equal to 3.872983346 and -3.872983346.Subproblem 1
p + -9 = 3.872983346 Simplifying p + -9 = 3.872983346 Reorder the terms: -9 + p = 3.872983346 Solving -9 + p = 3.872983346 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + p = 3.872983346 + 9 Combine like terms: -9 + 9 = 0 0 + p = 3.872983346 + 9 p = 3.872983346 + 9 Combine like terms: 3.872983346 + 9 = 12.872983346 p = 12.872983346 Simplifying p = 12.872983346Subproblem 2
p + -9 = -3.872983346 Simplifying p + -9 = -3.872983346 Reorder the terms: -9 + p = -3.872983346 Solving -9 + p = -3.872983346 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + p = -3.872983346 + 9 Combine like terms: -9 + 9 = 0 0 + p = -3.872983346 + 9 p = -3.872983346 + 9 Combine like terms: -3.872983346 + 9 = 5.127016654 p = 5.127016654 Simplifying p = 5.127016654Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.872983346, 5.127016654}
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