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Simplifying x4 + -6x2 = 8 Reorder the terms: -6x2 + x4 = 8 Solving -6x2 + x4 = 8 Solving for variable 'x'. Reorder the terms: -8 + -6x2 + x4 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + -6x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6x2 + x4 = 0 + 8 -6x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 -6x2 + x4 = 8 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = 8 + 9 Reorder the terms: 9 + -6x2 + x4 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6x2 + x4 = 17 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x2 + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
x2 + -3 = 4.123105626 Simplifying x2 + -3 = 4.123105626 Reorder the terms: -3 + x2 = 4.123105626 Solving -3 + x2 = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 4.123105626 + 3 x2 = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 x2 = 7.123105626 Simplifying x2 = 7.123105626 Take the square root of each side: x = {-2.668914691, 2.668914691}Subproblem 2
x2 + -3 = -4.123105626 Simplifying x2 + -3 = -4.123105626 Reorder the terms: -3 + x2 = -4.123105626 Solving -3 + x2 = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -4.123105626 + 3 x2 = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 x2 = -1.123105626 Simplifying x2 = -1.123105626 Reorder the terms: 1.123105626 + x2 = -1.123105626 + 1.123105626 Combine like terms: -1.123105626 + 1.123105626 = 0.000000000 1.123105626 + 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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