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Simplifying 3x4 + 4x2 + -3 = 0 Reorder the terms: -3 + 4x2 + 3x4 = 0 Solving -3 + 4x2 + 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'. -1 + 1.333333333x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.333333333x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + 1.333333333x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.333333333x2 + x4 = 0 + 1 1.333333333x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 1.333333333x2 + x4 = 1 The x term is 1.333333333x2. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x2 + 0.4444444442 + x4 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x2 + x4 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + 1.333333333x2 + x4 = 1.4444444442 Factor a perfect square on the left side: (x2 + 0.6666666665)(x2 + 0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x2 + 0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
x2 + 0.6666666665 = 1.201850425 Simplifying x2 + 0.6666666665 = 1.201850425 Reorder the terms: 0.6666666665 + x2 = 1.201850425 Solving 0.6666666665 + x2 = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x2 = 1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x2 = 1.201850425 + -0.6666666665 x2 = 1.201850425 + -0.6666666665 Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585 x2 = 0.5351837585 Simplifying x2 = 0.5351837585 Take the square root of each side: x = {-0.731562546, 0.731562546}Subproblem 2
x2 + 0.6666666665 = -1.201850425 Simplifying x2 + 0.6666666665 = -1.201850425 Reorder the terms: 0.6666666665 + x2 = -1.201850425 Solving 0.6666666665 + x2 = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x2 = -1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x2 = -1.201850425 + -0.6666666665 x2 = -1.201850425 + -0.6666666665 Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915 x2 = -1.8685170915 Simplifying x2 = -1.8685170915 Reorder the terms: 1.8685170915 + x2 = -1.8685170915 + 1.8685170915 Combine like terms: -1.8685170915 + 1.8685170915 = 0.0000000000 1.8685170915 + 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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