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Simplifying x2 + -18x + -1 = -6 Reorder the terms: -1 + -18x + x2 = -6 Solving -1 + -18x + x2 = -6 Solving for variable 'x'. Reorder the terms: -1 + 6 + -18x + x2 = -6 + 6 Combine like terms: -1 + 6 = 5 5 + -18x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 5 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -18x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -18x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -18x + x2 = 0 + -5 -18x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -18x + x2 = -5 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 = -5 + 81 Reorder the terms: 81 + -18x + x2 = -5 + 81 Combine like terms: -5 + 81 = 76 81 + -18x + x2 = 76 Factor a perfect square on the left side: (x + -9)(x + -9) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + -9) equal to 8.717797887 and -8.717797887.Subproblem 1
x + -9 = 8.717797887 Simplifying x + -9 = 8.717797887 Reorder the terms: -9 + x = 8.717797887 Solving -9 + x = 8.717797887 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 = 8.717797887 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.717797887 + 9 x = 8.717797887 + 9 Combine like terms: 8.717797887 + 9 = 17.717797887 x = 17.717797887 Simplifying x = 17.717797887Subproblem 2
x + -9 = -8.717797887 Simplifying x + -9 = -8.717797887 Reorder the terms: -9 + x = -8.717797887 Solving -9 + x = -8.717797887 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 = -8.717797887 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.717797887 + 9 x = -8.717797887 + 9 Combine like terms: -8.717797887 + 9 = 0.282202113 x = 0.282202113 Simplifying x = 0.282202113Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.717797887, 0.282202113}
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