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Simplifying 11x2 + -2x + -55 = 0 Reorder the terms: -55 + -2x + 11x2 = 0 Solving -55 + -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'. -5 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.1818181818x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.1818181818x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.1818181818x + x2 = 0 + 5 -0.1818181818x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.1818181818x + x2 = 5 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 = 5 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 5 + 0.008264462808 Combine like terms: 5 + 0.008264462808 = 5.008264462808 0.008264462808 + -0.1818181818x + x2 = 5.008264462808 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 5.008264462808 Calculate the square root of the right side: 2.237915205 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 2.237915205 and -2.237915205.Subproblem 1
x + -0.0909090909 = 2.237915205 Simplifying x + -0.0909090909 = 2.237915205 Reorder the terms: -0.0909090909 + x = 2.237915205 Solving -0.0909090909 + x = 2.237915205 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 = 2.237915205 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 2.237915205 + 0.0909090909 x = 2.237915205 + 0.0909090909 Combine like terms: 2.237915205 + 0.0909090909 = 2.3288242959 x = 2.3288242959 Simplifying x = 2.3288242959Subproblem 2
x + -0.0909090909 = -2.237915205 Simplifying x + -0.0909090909 = -2.237915205 Reorder the terms: -0.0909090909 + x = -2.237915205 Solving -0.0909090909 + x = -2.237915205 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 = -2.237915205 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -2.237915205 + 0.0909090909 x = -2.237915205 + 0.0909090909 Combine like terms: -2.237915205 + 0.0909090909 = -2.1470061141 x = -2.1470061141 Simplifying x = -2.1470061141Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3288242959, -2.1470061141}
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