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Simplifying 11x2 + 3x + -6 = 0 Reorder the terms: -6 + 3x + 11x2 = 0 Solving -6 + 3x + 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 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.2727272727x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + 0.2727272727x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + 0.2727272727x + x2 = 0 + 0.5454545455 0.2727272727x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 0.2727272727x + x2 = 0.5454545455 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 0.5454545455 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 0.5454545455 + 0.01859504133 Combine like terms: 0.5454545455 + 0.01859504133 = 0.56404958683 0.01859504133 + 0.2727272727x + x2 = 0.56404958683 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 0.56404958683 Calculate the square root of the right side: 0.751032347 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 0.751032347 and -0.751032347.Subproblem 1
x + 0.1363636364 = 0.751032347 Simplifying x + 0.1363636364 = 0.751032347 Reorder the terms: 0.1363636364 + x = 0.751032347 Solving 0.1363636364 + x = 0.751032347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 0.751032347 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 0.751032347 + -0.1363636364 x = 0.751032347 + -0.1363636364 Combine like terms: 0.751032347 + -0.1363636364 = 0.6146687106 x = 0.6146687106 Simplifying x = 0.6146687106Subproblem 2
x + 0.1363636364 = -0.751032347 Simplifying x + 0.1363636364 = -0.751032347 Reorder the terms: 0.1363636364 + x = -0.751032347 Solving 0.1363636364 + x = -0.751032347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -0.751032347 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -0.751032347 + -0.1363636364 x = -0.751032347 + -0.1363636364 Combine like terms: -0.751032347 + -0.1363636364 = -0.8873959834 x = -0.8873959834 Simplifying x = -0.8873959834Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6146687106, -0.8873959834}
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