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Simplifying x4 + x2 + 2x2 + 4 = 2x2 + 12 Reorder the terms: 4 + x2 + 2x2 + x4 = 2x2 + 12 Combine like terms: x2 + 2x2 = 3x2 4 + 3x2 + x4 = 2x2 + 12 Reorder the terms: 4 + 3x2 + x4 = 12 + 2x2 Solving 4 + 3x2 + x4 = 12 + 2x2 Solving for variable 'x'. Reorder the terms: 4 + -12 + 3x2 + -2x2 + x4 = 12 + 2x2 + -12 + -2x2 Combine like terms: 4 + -12 = -8 -8 + 3x2 + -2x2 + x4 = 12 + 2x2 + -12 + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -8 + 1x2 + x4 = 12 + 2x2 + -12 + -2x2 Reorder the terms: -8 + 1x2 + x4 = 12 + -12 + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -8 + 1x2 + x4 = 0 + 2x2 + -2x2 -8 + 1x2 + x4 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + 1x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 1x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + 1x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 1x2 + x4 = 0 + 8 1x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 1x2 + x4 = 8 The x term is 1x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 8 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 0.25 + x2 + x4 = 8.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x2 + 0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x2 + 0.5 = 2.872281323 Simplifying x2 + 0.5 = 2.872281323 Reorder the terms: 0.5 + x2 = 2.872281323 Solving 0.5 + x2 = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 2.872281323 + -0.5 x2 = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 x2 = 2.372281323 Simplifying x2 = 2.372281323 Take the square root of each side: x = {-1.540221193, 1.540221193}Subproblem 2
x2 + 0.5 = -2.872281323 Simplifying x2 + 0.5 = -2.872281323 Reorder the terms: 0.5 + x2 = -2.872281323 Solving 0.5 + x2 = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -2.872281323 + -0.5 x2 = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 x2 = -3.372281323 Simplifying x2 = -3.372281323 Reorder the terms: 3.372281323 + x2 = -3.372281323 + 3.372281323 Combine like terms: -3.372281323 + 3.372281323 = 0.000000000 3.372281323 + 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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