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Simplifying 3x4 + 5x2 + 1 = 0 Reorder the terms: 1 + 5x2 + 3x4 = 0 Solving 1 + 5x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 1.666666667x2 + x4 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.666666667x2 + -0.3333333333 + x4 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.666666667x2 + x4 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.666666667x2 + x4 = 0 + -0.3333333333 1.666666667x2 + x4 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.666666667x2 + x4 = -0.3333333333 The x term is 1.666666667x2. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x2 + 0.6944444447 + x4 = -0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x2 + x4 = -0.3333333333 + 0.6944444447 Combine like terms: -0.3333333333 + 0.6944444447 = 0.3611111114 0.6944444447 + 1.666666667x2 + x4 = 0.3611111114 Factor a perfect square on the left side: (x2 + 0.8333333335)(x2 + 0.8333333335) = 0.3611111114 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (x2 + 0.8333333335) equal to 0.600925213 and -0.600925213.Subproblem 1
x2 + 0.8333333335 = 0.600925213 Simplifying x2 + 0.8333333335 = 0.600925213 Reorder the terms: 0.8333333335 + x2 = 0.600925213 Solving 0.8333333335 + x2 = 0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = 0.600925213 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = 0.600925213 + -0.8333333335 x2 = 0.600925213 + -0.8333333335 Combine like terms: 0.600925213 + -0.8333333335 = -0.2324081205 x2 = -0.2324081205 Simplifying x2 = -0.2324081205 Reorder the terms: 0.2324081205 + x2 = -0.2324081205 + 0.2324081205 Combine like terms: -0.2324081205 + 0.2324081205 = 0.0000000000 0.2324081205 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 0.8333333335 = -0.600925213 Simplifying x2 + 0.8333333335 = -0.600925213 Reorder the terms: 0.8333333335 + x2 = -0.600925213 Solving 0.8333333335 + x2 = -0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = -0.600925213 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = -0.600925213 + -0.8333333335 x2 = -0.600925213 + -0.8333333335 Combine like terms: -0.600925213 + -0.8333333335 = -1.4342585465 x2 = -1.4342585465 Simplifying x2 = -1.4342585465 Reorder the terms: 1.4342585465 + x2 = -1.4342585465 + 1.4342585465 Combine like terms: -1.4342585465 + 1.4342585465 = 0.0000000000 1.4342585465 + x2 = 0.0000000000 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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