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Simplifying x4 + -12x2 + -11 = 0 Reorder the terms: -11 + -12x2 + x4 = 0 Solving -11 + -12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -12x2 + 11 + x4 = 0 + 11 Reorder the terms: -11 + 11 + -12x2 + x4 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -12x2 + x4 = 0 + 11 -12x2 + x4 = 0 + 11 Combine like terms: 0 + 11 = 11 -12x2 + x4 = 11 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = 11 + 36 Reorder the terms: 36 + -12x2 + x4 = 11 + 36 Combine like terms: 11 + 36 = 47 36 + -12x2 + x4 = 47 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x2 + -6) equal to 6.8556546 and -6.8556546.Subproblem 1
x2 + -6 = 6.8556546 Simplifying x2 + -6 = 6.8556546 Reorder the terms: -6 + x2 = 6.8556546 Solving -6 + x2 = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 6.8556546 + 6 x2 = 6.8556546 + 6 Combine like terms: 6.8556546 + 6 = 12.8556546 x2 = 12.8556546 Simplifying x2 = 12.8556546 Take the square root of each side: x = {-3.585478294, 3.585478294}Subproblem 2
x2 + -6 = -6.8556546 Simplifying x2 + -6 = -6.8556546 Reorder the terms: -6 + x2 = -6.8556546 Solving -6 + x2 = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -6.8556546 + 6 x2 = -6.8556546 + 6 Combine like terms: -6.8556546 + 6 = -0.8556546 x2 = -0.8556546 Simplifying x2 = -0.8556546 Reorder the terms: 0.8556546 + x2 = -0.8556546 + 0.8556546 Combine like terms: -0.8556546 + 0.8556546 = 0.0000000 0.8556546 + x2 = 0.0000000 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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