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Simplifying x2 + -18x = -15 Reorder the terms: -18x + x2 = -15 Solving -18x + x2 = -15 Solving for variable 'x'. Reorder the terms: 15 + -18x + x2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -18x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -18x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -18x + x2 = 0 + -15 -18x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -18x + x2 = -15 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -15 + 81 Reorder the terms: 81 + -18x + x2 = -15 + 81 Combine like terms: -15 + 81 = 66 81 + -18x + x2 = 66 Factor a perfect square on the left side: (x + -9)(x + -9) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + -9) equal to 8.124038405 and -8.124038405.Subproblem 1
x + -9 = 8.124038405 Simplifying x + -9 = 8.124038405 Reorder the terms: -9 + x = 8.124038405 Solving -9 + x = 8.124038405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.124038405 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.124038405 + 9 x = 8.124038405 + 9 Combine like terms: 8.124038405 + 9 = 17.124038405 x = 17.124038405 Simplifying x = 17.124038405Subproblem 2
x + -9 = -8.124038405 Simplifying x + -9 = -8.124038405 Reorder the terms: -9 + x = -8.124038405 Solving -9 + x = -8.124038405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.124038405 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.124038405 + 9 x = -8.124038405 + 9 Combine like terms: -8.124038405 + 9 = 0.875961595 x = 0.875961595 Simplifying x = 0.875961595Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.124038405, 0.875961595}
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