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Simplifying x4 + 24x2 + 48 = 0 Reorder the terms: 48 + 24x2 + x4 = 0 Solving 48 + 24x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 24x2 + -48 + x4 = 0 + -48 Reorder the terms: 48 + -48 + 24x2 + x4 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 24x2 + x4 = 0 + -48 24x2 + x4 = 0 + -48 Combine like terms: 0 + -48 = -48 24x2 + x4 = -48 The x term is 24x2. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x2 + 144 + x4 = -48 + 144 Reorder the terms: 144 + 24x2 + x4 = -48 + 144 Combine like terms: -48 + 144 = 96 144 + 24x2 + x4 = 96 Factor a perfect square on the left side: (x2 + 12)(x2 + 12) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x2 + 12) equal to 9.797958971 and -9.797958971.Subproblem 1
x2 + 12 = 9.797958971 Simplifying x2 + 12 = 9.797958971 Reorder the terms: 12 + x2 = 9.797958971 Solving 12 + x2 = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = 9.797958971 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 9.797958971 + -12 x2 = 9.797958971 + -12 Combine like terms: 9.797958971 + -12 = -2.202041029 x2 = -2.202041029 Simplifying x2 = -2.202041029 Reorder the terms: 2.202041029 + x2 = -2.202041029 + 2.202041029 Combine like terms: -2.202041029 + 2.202041029 = 0.000000000 2.202041029 + 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 + 12 = -9.797958971 Simplifying x2 + 12 = -9.797958971 Reorder the terms: 12 + x2 = -9.797958971 Solving 12 + x2 = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = -9.797958971 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = -9.797958971 + -12 x2 = -9.797958971 + -12 Combine like terms: -9.797958971 + -12 = -21.797958971 x2 = -21.797958971 Simplifying x2 = -21.797958971 Reorder the terms: 21.797958971 + x2 = -21.797958971 + 21.797958971 Combine like terms: -21.797958971 + 21.797958971 = 0.000000000 21.797958971 + 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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