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Simplifying x4 + 28x2 + 3 = 0 Reorder the terms: 3 + 28x2 + x4 = 0 Solving 3 + 28x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 28x2 + -3 + x4 = 0 + -3 Reorder the terms: 3 + -3 + 28x2 + x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 28x2 + x4 = 0 + -3 28x2 + x4 = 0 + -3 Combine like terms: 0 + -3 = -3 28x2 + x4 = -3 The x term is 28x2. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x2 + 196 + x4 = -3 + 196 Reorder the terms: 196 + 28x2 + x4 = -3 + 196 Combine like terms: -3 + 196 = 193 196 + 28x2 + x4 = 193 Factor a perfect square on the left side: (x2 + 14)(x2 + 14) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x2 + 14) equal to 13.892443989 and -13.892443989.Subproblem 1
x2 + 14 = 13.892443989 Simplifying x2 + 14 = 13.892443989 Reorder the terms: 14 + x2 = 13.892443989 Solving 14 + x2 = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x2 = 13.892443989 + -14 Combine like terms: 14 + -14 = 0 0 + x2 = 13.892443989 + -14 x2 = 13.892443989 + -14 Combine like terms: 13.892443989 + -14 = -0.107556011 x2 = -0.107556011 Simplifying x2 = -0.107556011 Reorder the terms: 0.107556011 + x2 = -0.107556011 + 0.107556011 Combine like terms: -0.107556011 + 0.107556011 = 0.000000000 0.107556011 + 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 + 14 = -13.892443989 Simplifying x2 + 14 = -13.892443989 Reorder the terms: 14 + x2 = -13.892443989 Solving 14 + x2 = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x2 = -13.892443989 + -14 Combine like terms: 14 + -14 = 0 0 + x2 = -13.892443989 + -14 x2 = -13.892443989 + -14 Combine like terms: -13.892443989 + -14 = -27.892443989 x2 = -27.892443989 Simplifying x2 = -27.892443989 Reorder the terms: 27.892443989 + x2 = -27.892443989 + 27.892443989 Combine like terms: -27.892443989 + 27.892443989 = 0.000000000 27.892443989 + 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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