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Simplifying 11x2 + 2x = 10 Reorder the terms: 2x + 11x2 = 10 Solving 2x + 11x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 2x + 11x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + 0.1818181818x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + 0.1818181818x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + 0.1818181818x + x2 = 0 + 0.9090909091 0.1818181818x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 0.1818181818x + x2 = 0.9090909091 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 = 0.9090909091 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 0.9090909091 + 0.008264462808 Combine like terms: 0.9090909091 + 0.008264462808 = 0.917355371908 0.008264462808 + 0.1818181818x + x2 = 0.917355371908 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 0.917355371908 Calculate the square root of the right side: 0.957786705 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 0.957786705 and -0.957786705.Subproblem 1
x + 0.0909090909 = 0.957786705 Simplifying x + 0.0909090909 = 0.957786705 Reorder the terms: 0.0909090909 + x = 0.957786705 Solving 0.0909090909 + x = 0.957786705 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 = 0.957786705 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 0.957786705 + -0.0909090909 x = 0.957786705 + -0.0909090909 Combine like terms: 0.957786705 + -0.0909090909 = 0.8668776141 x = 0.8668776141 Simplifying x = 0.8668776141Subproblem 2
x + 0.0909090909 = -0.957786705 Simplifying x + 0.0909090909 = -0.957786705 Reorder the terms: 0.0909090909 + x = -0.957786705 Solving 0.0909090909 + x = -0.957786705 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 = -0.957786705 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -0.957786705 + -0.0909090909 x = -0.957786705 + -0.0909090909 Combine like terms: -0.957786705 + -0.0909090909 = -1.0486957959 x = -1.0486957959 Simplifying x = -1.0486957959Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8668776141, -1.0486957959}
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