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Simplifying p2 + -18p + -116 = 10 Reorder the terms: -116 + -18p + p2 = 10 Solving -116 + -18p + p2 = 10 Solving for variable 'p'. Reorder the terms: -116 + -10 + -18p + p2 = 10 + -10 Combine like terms: -116 + -10 = -126 -126 + -18p + p2 = 10 + -10 Combine like terms: 10 + -10 = 0 -126 + -18p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + -18p + 126 + p2 = 0 + 126 Reorder the terms: -126 + 126 + -18p + p2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -18p + p2 = 0 + 126 -18p + p2 = 0 + 126 Combine like terms: 0 + 126 = 126 -18p + p2 = 126 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 = 126 + 81 Reorder the terms: 81 + -18p + p2 = 126 + 81 Combine like terms: 126 + 81 = 207 81 + -18p + p2 = 207 Factor a perfect square on the left side: (p + -9)(p + -9) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (p + -9) equal to 14.38749457 and -14.38749457.Subproblem 1
p + -9 = 14.38749457 Simplifying p + -9 = 14.38749457 Reorder the terms: -9 + p = 14.38749457 Solving -9 + p = 14.38749457 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 = 14.38749457 + 9 Combine like terms: -9 + 9 = 0 0 + p = 14.38749457 + 9 p = 14.38749457 + 9 Combine like terms: 14.38749457 + 9 = 23.38749457 p = 23.38749457 Simplifying p = 23.38749457Subproblem 2
p + -9 = -14.38749457 Simplifying p + -9 = -14.38749457 Reorder the terms: -9 + p = -14.38749457 Solving -9 + p = -14.38749457 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 = -14.38749457 + 9 Combine like terms: -9 + 9 = 0 0 + p = -14.38749457 + 9 p = -14.38749457 + 9 Combine like terms: -14.38749457 + 9 = -5.38749457 p = -5.38749457 Simplifying p = -5.38749457Solution
The solution to the problem is based on the solutions from the subproblems. p = {23.38749457, -5.38749457}
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