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Simplifying 11x2 + -33x + -398 = 0 Reorder the terms: -398 + -33x + 11x2 = 0 Solving -398 + -33x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -36.18181818 + -3x + x2 = 0 Move the constant term to the right: Add '36.18181818' to each side of the equation. -36.18181818 + -3x + 36.18181818 + x2 = 0 + 36.18181818 Reorder the terms: -36.18181818 + 36.18181818 + -3x + x2 = 0 + 36.18181818 Combine like terms: -36.18181818 + 36.18181818 = 0.00000000 0.00000000 + -3x + x2 = 0 + 36.18181818 -3x + x2 = 0 + 36.18181818 Combine like terms: 0 + 36.18181818 = 36.18181818 -3x + x2 = 36.18181818 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 36.18181818 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 36.18181818 + 2.25 Combine like terms: 36.18181818 + 2.25 = 38.43181818 2.25 + -3x + x2 = 38.43181818 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 38.43181818 Calculate the square root of the right side: 6.199340141 Break this problem into two subproblems by setting (x + -1.5) equal to 6.199340141 and -6.199340141.Subproblem 1
x + -1.5 = 6.199340141 Simplifying x + -1.5 = 6.199340141 Reorder the terms: -1.5 + x = 6.199340141 Solving -1.5 + x = 6.199340141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.199340141 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.199340141 + 1.5 x = 6.199340141 + 1.5 Combine like terms: 6.199340141 + 1.5 = 7.699340141 x = 7.699340141 Simplifying x = 7.699340141Subproblem 2
x + -1.5 = -6.199340141 Simplifying x + -1.5 = -6.199340141 Reorder the terms: -1.5 + x = -6.199340141 Solving -1.5 + x = -6.199340141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.199340141 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.199340141 + 1.5 x = -6.199340141 + 1.5 Combine like terms: -6.199340141 + 1.5 = -4.699340141 x = -4.699340141 Simplifying x = -4.699340141Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.699340141, -4.699340141}
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