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Simplifying p2 + -18p + 71 = 0 Reorder the terms: 71 + -18p + p2 = 0 Solving 71 + -18p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-71' to each side of the equation. 71 + -18p + -71 + p2 = 0 + -71 Reorder the terms: 71 + -71 + -18p + p2 = 0 + -71 Combine like terms: 71 + -71 = 0 0 + -18p + p2 = 0 + -71 -18p + p2 = 0 + -71 Combine like terms: 0 + -71 = -71 -18p + p2 = -71 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 = -71 + 81 Reorder the terms: 81 + -18p + p2 = -71 + 81 Combine like terms: -71 + 81 = 10 81 + -18p + p2 = 10 Factor a perfect square on the left side: (p + -9)(p + -9) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (p + -9) equal to 3.16227766 and -3.16227766.Subproblem 1
p + -9 = 3.16227766 Simplifying p + -9 = 3.16227766 Reorder the terms: -9 + p = 3.16227766 Solving -9 + p = 3.16227766 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 = 3.16227766 + 9 Combine like terms: -9 + 9 = 0 0 + p = 3.16227766 + 9 p = 3.16227766 + 9 Combine like terms: 3.16227766 + 9 = 12.16227766 p = 12.16227766 Simplifying p = 12.16227766Subproblem 2
p + -9 = -3.16227766 Simplifying p + -9 = -3.16227766 Reorder the terms: -9 + p = -3.16227766 Solving -9 + p = -3.16227766 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 = -3.16227766 + 9 Combine like terms: -9 + 9 = 0 0 + p = -3.16227766 + 9 p = -3.16227766 + 9 Combine like terms: -3.16227766 + 9 = 5.83772234 p = 5.83772234 Simplifying p = 5.83772234Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.16227766, 5.83772234}
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