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Simplifying x2 + -18x + 8 = 0 Reorder the terms: 8 + -18x + x2 = 0 Solving 8 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -18x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -18x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -18x + x2 = 0 + -8 -18x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -18x + x2 = -8 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 = -8 + 81 Reorder the terms: 81 + -18x + x2 = -8 + 81 Combine like terms: -8 + 81 = 73 81 + -18x + x2 = 73 Factor a perfect square on the left side: (x + -9)(x + -9) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -9) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -9 = 8.544003745 Simplifying x + -9 = 8.544003745 Reorder the terms: -9 + x = 8.544003745 Solving -9 + x = 8.544003745 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 = 8.544003745 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.544003745 + 9 x = 8.544003745 + 9 Combine like terms: 8.544003745 + 9 = 17.544003745 x = 17.544003745 Simplifying x = 17.544003745Subproblem 2
x + -9 = -8.544003745 Simplifying x + -9 = -8.544003745 Reorder the terms: -9 + x = -8.544003745 Solving -9 + x = -8.544003745 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 = -8.544003745 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.544003745 + 9 x = -8.544003745 + 9 Combine like terms: -8.544003745 + 9 = 0.455996255 x = 0.455996255 Simplifying x = 0.455996255Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.544003745, 0.455996255}
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