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Simplifying 2x2 + -33x + 55 = 0 Reorder the terms: 55 + -33x + 2x2 = 0 Solving 55 + -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'. 27.5 + -16.5x + x2 = 0 Move the constant term to the right: Add '-27.5' to each side of the equation. 27.5 + -16.5x + -27.5 + x2 = 0 + -27.5 Reorder the terms: 27.5 + -27.5 + -16.5x + x2 = 0 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + -16.5x + x2 = 0 + -27.5 -16.5x + x2 = 0 + -27.5 Combine like terms: 0 + -27.5 = -27.5 -16.5x + x2 = -27.5 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 = -27.5 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -27.5 + 68.0625 Combine like terms: -27.5 + 68.0625 = 40.5625 68.0625 + -16.5x + x2 = 40.5625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 40.5625 Calculate the square root of the right side: 6.368869601 Break this problem into two subproblems by setting (x + -8.25) equal to 6.368869601 and -6.368869601.Subproblem 1
x + -8.25 = 6.368869601 Simplifying x + -8.25 = 6.368869601 Reorder the terms: -8.25 + x = 6.368869601 Solving -8.25 + x = 6.368869601 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 = 6.368869601 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 6.368869601 + 8.25 x = 6.368869601 + 8.25 Combine like terms: 6.368869601 + 8.25 = 14.618869601 x = 14.618869601 Simplifying x = 14.618869601Subproblem 2
x + -8.25 = -6.368869601 Simplifying x + -8.25 = -6.368869601 Reorder the terms: -8.25 + x = -6.368869601 Solving -8.25 + x = -6.368869601 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 = -6.368869601 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -6.368869601 + 8.25 x = -6.368869601 + 8.25 Combine like terms: -6.368869601 + 8.25 = 1.881130399 x = 1.881130399 Simplifying x = 1.881130399Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.618869601, 1.881130399}
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