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Simplifying (x2) + 18x = -15 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 = -0.875961595 x = -0.875961595 Simplifying x = -0.875961595Subproblem 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 = -17.124038405 x = -17.124038405 Simplifying x = -17.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.875961595, -17.124038405}
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