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Simplifying 6x4 + -6x2 + -11 = 0 Reorder the terms: -11 + -6x2 + 6x4 = 0 Solving -11 + -6x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -1x2 + x4 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -1x2 + 1.833333333 + x4 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -1x2 + x4 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -1x2 + x4 = 0 + 1.833333333 -1x2 + x4 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -1x2 + x4 = 1.833333333 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = 1.833333333 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 1.833333333 + 0.25 Combine like terms: 1.833333333 + 0.25 = 2.083333333 0.25 + -1x2 + x4 = 2.083333333 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 2.083333333 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (x2 + -0.5) equal to 1.443375673 and -1.443375673.Subproblem 1
x2 + -0.5 = 1.443375673 Simplifying x2 + -0.5 = 1.443375673 Reorder the terms: -0.5 + x2 = 1.443375673 Solving -0.5 + x2 = 1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 1.443375673 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 1.443375673 + 0.5 x2 = 1.443375673 + 0.5 Combine like terms: 1.443375673 + 0.5 = 1.943375673 x2 = 1.943375673 Simplifying x2 = 1.943375673 Take the square root of each side: x = {-1.394050097, 1.394050097}Subproblem 2
x2 + -0.5 = -1.443375673 Simplifying x2 + -0.5 = -1.443375673 Reorder the terms: -0.5 + x2 = -1.443375673 Solving -0.5 + x2 = -1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -1.443375673 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -1.443375673 + 0.5 x2 = -1.443375673 + 0.5 Combine like terms: -1.443375673 + 0.5 = -0.943375673 x2 = -0.943375673 Simplifying x2 = -0.943375673 Reorder the terms: 0.943375673 + x2 = -0.943375673 + 0.943375673 Combine like terms: -0.943375673 + 0.943375673 = 0.000000000 0.943375673 + x2 = 0.000000000 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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