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Simplifying 11x2 + -10x + -6 = 0 Reorder the terms: -6 + -10x + 11x2 = 0 Solving -6 + -10x + 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'. -0.5454545455 + -0.9090909091x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -0.9090909091x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -0.9090909091x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -0.9090909091x + x2 = 0 + 0.5454545455 -0.9090909091x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -0.9090909091x + x2 = 0.5454545455 The x term is -0.9090909091x. Take half its coefficient (-0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. -0.9090909091x + 0.2066115703 + x2 = 0.5454545455 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091x + x2 = 0.5454545455 + 0.2066115703 Combine like terms: 0.5454545455 + 0.2066115703 = 0.7520661158 0.2066115703 + -0.9090909091x + x2 = 0.7520661158 Factor a perfect square on the left side: (x + -0.4545454546)(x + -0.4545454546) = 0.7520661158 Calculate the square root of the right side: 0.867217456 Break this problem into two subproblems by setting (x + -0.4545454546) equal to 0.867217456 and -0.867217456.Subproblem 1
x + -0.4545454546 = 0.867217456 Simplifying x + -0.4545454546 = 0.867217456 Reorder the terms: -0.4545454546 + x = 0.867217456 Solving -0.4545454546 + x = 0.867217456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = 0.867217456 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = 0.867217456 + 0.4545454546 x = 0.867217456 + 0.4545454546 Combine like terms: 0.867217456 + 0.4545454546 = 1.3217629106 x = 1.3217629106 Simplifying x = 1.3217629106Subproblem 2
x + -0.4545454546 = -0.867217456 Simplifying x + -0.4545454546 = -0.867217456 Reorder the terms: -0.4545454546 + x = -0.867217456 Solving -0.4545454546 + x = -0.867217456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = -0.867217456 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = -0.867217456 + 0.4545454546 x = -0.867217456 + 0.4545454546 Combine like terms: -0.867217456 + 0.4545454546 = -0.4126720014 x = -0.4126720014 Simplifying x = -0.4126720014Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3217629106, -0.4126720014}
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