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Simplifying x2 + -33x + -1 = 0 Reorder the terms: -1 + -33x + x2 = 0 Solving -1 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -33x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -33x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -33x + x2 = 0 + 1 -33x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -33x + x2 = 1 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 = 1 + 272.25 Reorder the terms: 272.25 + -33x + x2 = 1 + 272.25 Combine like terms: 1 + 272.25 = 273.25 272.25 + -33x + x2 = 273.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 273.25 Calculate the square root of the right side: 16.530275255 Break this problem into two subproblems by setting (x + -16.5) equal to 16.530275255 and -16.530275255.Subproblem 1
x + -16.5 = 16.530275255 Simplifying x + -16.5 = 16.530275255 Reorder the terms: -16.5 + x = 16.530275255 Solving -16.5 + x = 16.530275255 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 = 16.530275255 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 16.530275255 + 16.5 x = 16.530275255 + 16.5 Combine like terms: 16.530275255 + 16.5 = 33.030275255 x = 33.030275255 Simplifying x = 33.030275255Subproblem 2
x + -16.5 = -16.530275255 Simplifying x + -16.5 = -16.530275255 Reorder the terms: -16.5 + x = -16.530275255 Solving -16.5 + x = -16.530275255 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 = -16.530275255 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -16.530275255 + 16.5 x = -16.530275255 + 16.5 Combine like terms: -16.530275255 + 16.5 = -0.030275255 x = -0.030275255 Simplifying x = -0.030275255Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.030275255, -0.030275255}
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