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Simplifying -1x4 + -11x2 + -6 = 0 Reorder the terms: -6 + -11x2 + -1x4 = 0 Solving -6 + -11x2 + -1x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 11x2 + x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 11x2 + x4)' equal to zero and attempt to solve: Simplifying 6 + 11x2 + x4 = 0 Solving 6 + 11x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 11x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + 11x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 11x2 + x4 = 0 + -6 11x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 11x2 + x4 = -6 The x term is 11x2. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x2 + 30.25 + x4 = -6 + 30.25 Reorder the terms: 30.25 + 11x2 + x4 = -6 + 30.25 Combine like terms: -6 + 30.25 = 24.25 30.25 + 11x2 + x4 = 24.25 Factor a perfect square on the left side: (x2 + 5.5)(x2 + 5.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x2 + 5.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x2 + 5.5 = 4.924428901 Simplifying x2 + 5.5 = 4.924428901 Reorder the terms: 5.5 + x2 = 4.924428901 Solving 5.5 + x2 = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x2 = 4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = 4.924428901 + -5.5 x2 = 4.924428901 + -5.5 Combine like terms: 4.924428901 + -5.5 = -0.575571099 x2 = -0.575571099 Simplifying x2 = -0.575571099 Reorder the terms: 0.575571099 + x2 = -0.575571099 + 0.575571099 Combine like terms: -0.575571099 + 0.575571099 = 0.000000000 0.575571099 + x2 = 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
x2 + 5.5 = -4.924428901 Simplifying x2 + 5.5 = -4.924428901 Reorder the terms: 5.5 + x2 = -4.924428901 Solving 5.5 + x2 = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x2 = -4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = -4.924428901 + -5.5 x2 = -4.924428901 + -5.5 Combine like terms: -4.924428901 + -5.5 = -10.424428901 x2 = -10.424428901 Simplifying x2 = -10.424428901 Reorder the terms: 10.424428901 + x2 = -10.424428901 + 10.424428901 Combine like terms: -10.424428901 + 10.424428901 = 0.000000000 10.424428901 + 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. 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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