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Simplifying 11x4 + -1x2 + -6 = 0 Reorder the terms: -6 + -1x2 + 11x4 = 0 Solving -6 + -1x2 + 11x4 = 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 + -0.09090909091x2 + x4 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -0.09090909091x2 + 0.5454545455 + x4 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -0.09090909091x2 + x4 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -0.09090909091x2 + x4 = 0 + 0.5454545455 -0.09090909091x2 + x4 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -0.09090909091x2 + x4 = 0.5454545455 The x term is -0.09090909091x2. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091x2 + 0.002066115703 + x4 = 0.5454545455 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091x2 + x4 = 0.5454545455 + 0.002066115703 Combine like terms: 0.5454545455 + 0.002066115703 = 0.547520661203 0.002066115703 + -0.09090909091x2 + x4 = 0.547520661203 Factor a perfect square on the left side: (x2 + -0.04545454546)(x2 + -0.04545454546) = 0.547520661203 Calculate the square root of the right side: 0.739946391 Break this problem into two subproblems by setting (x2 + -0.04545454546) equal to 0.739946391 and -0.739946391.Subproblem 1
x2 + -0.04545454546 = 0.739946391 Simplifying x2 + -0.04545454546 = 0.739946391 Reorder the terms: -0.04545454546 + x2 = 0.739946391 Solving -0.04545454546 + x2 = 0.739946391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x2 = 0.739946391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x2 = 0.739946391 + 0.04545454546 x2 = 0.739946391 + 0.04545454546 Combine like terms: 0.739946391 + 0.04545454546 = 0.78540093646 x2 = 0.78540093646 Simplifying x2 = 0.78540093646 Take the square root of each side: x = {-0.88622849, 0.88622849}Subproblem 2
x2 + -0.04545454546 = -0.739946391 Simplifying x2 + -0.04545454546 = -0.739946391 Reorder the terms: -0.04545454546 + x2 = -0.739946391 Solving -0.04545454546 + x2 = -0.739946391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x2 = -0.739946391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x2 = -0.739946391 + 0.04545454546 x2 = -0.739946391 + 0.04545454546 Combine like terms: -0.739946391 + 0.04545454546 = -0.69449184554 x2 = -0.69449184554 Simplifying x2 = -0.69449184554 Reorder the terms: 0.69449184554 + x2 = -0.69449184554 + 0.69449184554 Combine like terms: -0.69449184554 + 0.69449184554 = 0.00000000000 0.69449184554 + x2 = 0.00000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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