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Simplifying -1(11x2 + 2x + -1) = 0 Reorder the terms: -1(-1 + 2x + 11x2) = 0 (-1 * -1 + 2x * -1 + 11x2 * -1) = 0 (1 + -2x + -11x2) = 0 Solving 1 + -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'. -0.09090909091 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + 0.1818181818x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + 0.1818181818x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + 0.1818181818x + x2 = 0 + 0.09090909091 0.1818181818x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 0.1818181818x + x2 = 0.09090909091 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 = 0.09090909091 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 0.09090909091 + 0.008264462808 Combine like terms: 0.09090909091 + 0.008264462808 = 0.099173553718 0.008264462808 + 0.1818181818x + x2 = 0.099173553718 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 0.099173553718 Calculate the square root of the right side: 0.314918329 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 0.314918329 and -0.314918329.Subproblem 1
x + 0.0909090909 = 0.314918329 Simplifying x + 0.0909090909 = 0.314918329 Reorder the terms: 0.0909090909 + x = 0.314918329 Solving 0.0909090909 + x = 0.314918329 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 = 0.314918329 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 0.314918329 + -0.0909090909 x = 0.314918329 + -0.0909090909 Combine like terms: 0.314918329 + -0.0909090909 = 0.2240092381 x = 0.2240092381 Simplifying x = 0.2240092381Subproblem 2
x + 0.0909090909 = -0.314918329 Simplifying x + 0.0909090909 = -0.314918329 Reorder the terms: 0.0909090909 + x = -0.314918329 Solving 0.0909090909 + x = -0.314918329 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 = -0.314918329 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -0.314918329 + -0.0909090909 x = -0.314918329 + -0.0909090909 Combine like terms: -0.314918329 + -0.0909090909 = -0.4058274199 x = -0.4058274199 Simplifying x = -0.4058274199Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2240092381, -0.4058274199}
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