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Simplifying 3x2 + -33x + -44 = 0 Reorder the terms: -44 + -33x + 3x2 = 0 Solving -44 + -33x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + -11x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + -11x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + -11x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + -11x + x2 = 0 + 14.66666667 -11x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 -11x + x2 = 14.66666667 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 14.66666667 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 14.66666667 + 30.25 Combine like terms: 14.66666667 + 30.25 = 44.91666667 30.25 + -11x + x2 = 44.91666667 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 44.91666667 Calculate the square root of the right side: 6.701989755 Break this problem into two subproblems by setting (x + -5.5) equal to 6.701989755 and -6.701989755.Subproblem 1
x + -5.5 = 6.701989755 Simplifying x + -5.5 = 6.701989755 Reorder the terms: -5.5 + x = 6.701989755 Solving -5.5 + x = 6.701989755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.701989755 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.701989755 + 5.5 x = 6.701989755 + 5.5 Combine like terms: 6.701989755 + 5.5 = 12.201989755 x = 12.201989755 Simplifying x = 12.201989755Subproblem 2
x + -5.5 = -6.701989755 Simplifying x + -5.5 = -6.701989755 Reorder the terms: -5.5 + x = -6.701989755 Solving -5.5 + x = -6.701989755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.701989755 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.701989755 + 5.5 x = -6.701989755 + 5.5 Combine like terms: -6.701989755 + 5.5 = -1.201989755 x = -1.201989755 Simplifying x = -1.201989755Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.201989755, -1.201989755}
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