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Simplifying 2x2 + -33x + -81 = 0 Reorder the terms: -81 + -33x + 2x2 = 0 Solving -81 + -33x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + -16.5x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + -16.5x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + -16.5x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + -16.5x + x2 = 0 + 40.5 -16.5x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 -16.5x + x2 = 40.5 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = 40.5 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = 40.5 + 68.0625 Combine like terms: 40.5 + 68.0625 = 108.5625 68.0625 + -16.5x + x2 = 108.5625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 108.5625 Calculate the square root of the right side: 10.419332992 Break this problem into two subproblems by setting (x + -8.25) equal to 10.419332992 and -10.419332992.Subproblem 1
x + -8.25 = 10.419332992 Simplifying x + -8.25 = 10.419332992 Reorder the terms: -8.25 + x = 10.419332992 Solving -8.25 + x = 10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 10.419332992 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 10.419332992 + 8.25 x = 10.419332992 + 8.25 Combine like terms: 10.419332992 + 8.25 = 18.669332992 x = 18.669332992 Simplifying x = 18.669332992Subproblem 2
x + -8.25 = -10.419332992 Simplifying x + -8.25 = -10.419332992 Reorder the terms: -8.25 + x = -10.419332992 Solving -8.25 + x = -10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -10.419332992 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -10.419332992 + 8.25 x = -10.419332992 + 8.25 Combine like terms: -10.419332992 + 8.25 = -2.169332992 x = -2.169332992 Simplifying x = -2.169332992Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.669332992, -2.169332992}
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