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Simplifying 11x2 + 2x = 11 Reorder the terms: 2x + 11x2 = 11 Solving 2x + 11x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 2x + 11x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1818181818x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1818181818x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1818181818x + x2 = 0 + 1 0.1818181818x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1818181818x + x2 = 1 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 = 1 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 1 + 0.008264462808 Combine like terms: 1 + 0.008264462808 = 1.008264462808 0.008264462808 + 0.1818181818x + x2 = 1.008264462808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 1.008264462808 Calculate the square root of the right side: 1.004123729 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 1.004123729 and -1.004123729.Subproblem 1
x + 0.0909090909 = 1.004123729 Simplifying x + 0.0909090909 = 1.004123729 Reorder the terms: 0.0909090909 + x = 1.004123729 Solving 0.0909090909 + x = 1.004123729 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 = 1.004123729 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.004123729 + -0.0909090909 x = 1.004123729 + -0.0909090909 Combine like terms: 1.004123729 + -0.0909090909 = 0.9132146381 x = 0.9132146381 Simplifying x = 0.9132146381Subproblem 2
x + 0.0909090909 = -1.004123729 Simplifying x + 0.0909090909 = -1.004123729 Reorder the terms: 0.0909090909 + x = -1.004123729 Solving 0.0909090909 + x = -1.004123729 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 = -1.004123729 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.004123729 + -0.0909090909 x = -1.004123729 + -0.0909090909 Combine like terms: -1.004123729 + -0.0909090909 = -1.0950328199 x = -1.0950328199 Simplifying x = -1.0950328199Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9132146381, -1.0950328199}
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