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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 = 1.027777778 0.6944444447 + 1.666666667x2 + x4 = 1.027777778 Factor a perfect square on the left side: (x2 + 0.8333333335)(x2 + 0.8333333335) = 1.027777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x2 + 0.8333333335) equal to 1.013793755 and -1.013793755.Subproblem 1
x2 + 0.8333333335 = 1.013793755 Simplifying x2 + 0.8333333335 = 1.013793755 Reorder the terms: 0.8333333335 + x2 = 1.013793755 Solving 0.8333333335 + x2 = 1.013793755 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 = 1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = 1.013793755 + -0.8333333335 x2 = 1.013793755 + -0.8333333335 Combine like terms: 1.013793755 + -0.8333333335 = 0.1804604215 x2 = 0.1804604215 Simplifying x2 = 0.1804604215 Take the square root of each side: x = {-0.424806334, 0.424806334}Subproblem 2
x2 + 0.8333333335 = -1.013793755 Simplifying x2 + 0.8333333335 = -1.013793755 Reorder the terms: 0.8333333335 + x2 = -1.013793755 Solving 0.8333333335 + x2 = -1.013793755 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 = -1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = -1.013793755 + -0.8333333335 x2 = -1.013793755 + -0.8333333335 Combine like terms: -1.013793755 + -0.8333333335 = -1.8471270885 x2 = -1.8471270885 Simplifying x2 = -1.8471270885 Reorder the terms: 1.8471270885 + x2 = -1.8471270885 + 1.8471270885 Combine like terms: -1.8471270885 + 1.8471270885 = 0.0000000000 1.8471270885 + 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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