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Simplifying 11x2 + -2x + -5 = 0 Reorder the terms: -5 + -2x + 11x2 = 0 Solving -5 + -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'. -0.4545454545 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -0.1818181818x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -0.1818181818x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -0.1818181818x + x2 = 0 + 0.4545454545 -0.1818181818x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -0.1818181818x + x2 = 0.4545454545 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 = 0.4545454545 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 0.4545454545 + 0.008264462808 Combine like terms: 0.4545454545 + 0.008264462808 = 0.462809917308 0.008264462808 + -0.1818181818x + x2 = 0.462809917308 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 0.462809917308 Calculate the square root of the right side: 0.680301343 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 0.680301343 and -0.680301343.Subproblem 1
x + -0.0909090909 = 0.680301343 Simplifying x + -0.0909090909 = 0.680301343 Reorder the terms: -0.0909090909 + x = 0.680301343 Solving -0.0909090909 + x = 0.680301343 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 = 0.680301343 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 0.680301343 + 0.0909090909 x = 0.680301343 + 0.0909090909 Combine like terms: 0.680301343 + 0.0909090909 = 0.7712104339 x = 0.7712104339 Simplifying x = 0.7712104339Subproblem 2
x + -0.0909090909 = -0.680301343 Simplifying x + -0.0909090909 = -0.680301343 Reorder the terms: -0.0909090909 + x = -0.680301343 Solving -0.0909090909 + x = -0.680301343 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 = -0.680301343 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -0.680301343 + 0.0909090909 x = -0.680301343 + 0.0909090909 Combine like terms: -0.680301343 + 0.0909090909 = -0.5893922521 x = -0.5893922521 Simplifying x = -0.5893922521Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7712104339, -0.5893922521}
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