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Simplifying x2 + -33x + 18 = 0 Reorder the terms: 18 + -33x + x2 = 0 Solving 18 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -33x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -33x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -33x + x2 = 0 + -18 -33x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -33x + x2 = -18 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -18 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -18 + 272.25 Combine like terms: -18 + 272.25 = 254.25 272.25 + -33x + x2 = 254.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + -16.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + -16.5 = 15.945218719 Simplifying x + -16.5 = 15.945218719 Reorder the terms: -16.5 + x = 15.945218719 Solving -16.5 + x = 15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 15.945218719 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 15.945218719 + 16.5 x = 15.945218719 + 16.5 Combine like terms: 15.945218719 + 16.5 = 32.445218719 x = 32.445218719 Simplifying x = 32.445218719Subproblem 2
x + -16.5 = -15.945218719 Simplifying x + -16.5 = -15.945218719 Reorder the terms: -16.5 + x = -15.945218719 Solving -16.5 + x = -15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -15.945218719 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -15.945218719 + 16.5 x = -15.945218719 + 16.5 Combine like terms: -15.945218719 + 16.5 = 0.554781281 x = 0.554781281 Simplifying x = 0.554781281Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.445218719, 0.554781281}
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