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Simplifying 11x2 + 2x + -34 = 0 Reorder the terms: -34 + 2x + 11x2 = 0 Solving -34 + 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'. -3.090909091 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '3.090909091' to each side of the equation. -3.090909091 + 0.1818181818x + 3.090909091 + x2 = 0 + 3.090909091 Reorder the terms: -3.090909091 + 3.090909091 + 0.1818181818x + x2 = 0 + 3.090909091 Combine like terms: -3.090909091 + 3.090909091 = 0.000000000 0.000000000 + 0.1818181818x + x2 = 0 + 3.090909091 0.1818181818x + x2 = 0 + 3.090909091 Combine like terms: 0 + 3.090909091 = 3.090909091 0.1818181818x + x2 = 3.090909091 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 = 3.090909091 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 3.090909091 + 0.008264462808 Combine like terms: 3.090909091 + 0.008264462808 = 3.099173553808 0.008264462808 + 0.1818181818x + x2 = 3.099173553808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 3.099173553808 Calculate the square root of the right side: 1.760446976 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 1.760446976 and -1.760446976.Subproblem 1
x + 0.0909090909 = 1.760446976 Simplifying x + 0.0909090909 = 1.760446976 Reorder the terms: 0.0909090909 + x = 1.760446976 Solving 0.0909090909 + x = 1.760446976 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 = 1.760446976 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.760446976 + -0.0909090909 x = 1.760446976 + -0.0909090909 Combine like terms: 1.760446976 + -0.0909090909 = 1.6695378851 x = 1.6695378851 Simplifying x = 1.6695378851Subproblem 2
x + 0.0909090909 = -1.760446976 Simplifying x + 0.0909090909 = -1.760446976 Reorder the terms: 0.0909090909 + x = -1.760446976 Solving 0.0909090909 + x = -1.760446976 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 = -1.760446976 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.760446976 + -0.0909090909 x = -1.760446976 + -0.0909090909 Combine like terms: -1.760446976 + -0.0909090909 = -1.8513560669 x = -1.8513560669 Simplifying x = -1.8513560669Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6695378851, -1.8513560669}
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