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Simplifying 11x2 + 2x + -33 = 0 Reorder the terms: -33 + 2x + 11x2 = 0 Solving -33 + 2x + 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'. -3 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.1818181818x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.1818181818x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.1818181818x + x2 = 0 + 3 0.1818181818x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.1818181818x + x2 = 3 The x term is 0.1818181818x. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818x + 0.008264462808 + x2 = 3 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 3 + 0.008264462808 Combine like terms: 3 + 0.008264462808 = 3.008264462808 0.008264462808 + 0.1818181818x + x2 = 3.008264462808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 3.008264462808 Calculate the square root of the right side: 1.734434912 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 1.734434912 and -1.734434912.Subproblem 1
x + 0.0909090909 = 1.734434912 Simplifying x + 0.0909090909 = 1.734434912 Reorder the terms: 0.0909090909 + x = 1.734434912 Solving 0.0909090909 + x = 1.734434912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 1.734434912 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.734434912 + -0.0909090909 x = 1.734434912 + -0.0909090909 Combine like terms: 1.734434912 + -0.0909090909 = 1.6435258211 x = 1.6435258211 Simplifying x = 1.6435258211Subproblem 2
x + 0.0909090909 = -1.734434912 Simplifying x + 0.0909090909 = -1.734434912 Reorder the terms: 0.0909090909 + x = -1.734434912 Solving 0.0909090909 + x = -1.734434912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -1.734434912 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.734434912 + -0.0909090909 x = -1.734434912 + -0.0909090909 Combine like terms: -1.734434912 + -0.0909090909 = -1.8253440029 x = -1.8253440029 Simplifying x = -1.8253440029Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6435258211, -1.8253440029}
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