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Simplifying x8 + -12x4 + -2 = 0 Reorder the terms: -2 + -12x4 + x8 = 0 Solving -2 + -12x4 + x8 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -12x4 + 2 + x8 = 0 + 2 Reorder the terms: -2 + 2 + -12x4 + x8 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -12x4 + x8 = 0 + 2 -12x4 + x8 = 0 + 2 Combine like terms: 0 + 2 = 2 -12x4 + x8 = 2 The x term is -12x4. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x4 + 36 + x8 = 2 + 36 Reorder the terms: 36 + -12x4 + x8 = 2 + 36 Combine like terms: 2 + 36 = 38 36 + -12x4 + x8 = 38 Factor a perfect square on the left side: (x4 + -6)(x4 + -6) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x4 + -6) equal to 6.164414003 and -6.164414003.Subproblem 1
x4 + -6 = 6.164414003 Simplifying x4 + -6 = 6.164414003 Reorder the terms: -6 + x4 = 6.164414003 Solving -6 + x4 = 6.164414003 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 + x4 = 6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + x4 = 6.164414003 + 6 x4 = 6.164414003 + 6 Combine like terms: 6.164414003 + 6 = 12.164414003 x4 = 12.164414003 Simplifying x4 = 12.164414003 Reorder the terms: -12.164414003 + x4 = 12.164414003 + -12.164414003 Combine like terms: 12.164414003 + -12.164414003 = 0.000000000 -12.164414003 + x4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x4 + -6 = -6.164414003 Simplifying x4 + -6 = -6.164414003 Reorder the terms: -6 + x4 = -6.164414003 Solving -6 + x4 = -6.164414003 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 + x4 = -6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + x4 = -6.164414003 + 6 x4 = -6.164414003 + 6 Combine like terms: -6.164414003 + 6 = -0.164414003 x4 = -0.164414003 Simplifying x4 = -0.164414003 Reorder the terms: 0.164414003 + x4 = -0.164414003 + 0.164414003 Combine like terms: -0.164414003 + 0.164414003 = 0.000000000 0.164414003 + x4 = 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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