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Simplifying 46x4 + 92x2 + 4 = 0 Reorder the terms: 4 + 92x2 + 46x4 = 0 Solving 4 + 92x2 + 46x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 46x2 + 23x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 46x2 + 23x4)' equal to zero and attempt to solve: Simplifying 2 + 46x2 + 23x4 = 0 Solving 2 + 46x2 + 23x4 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 0.08695652174 + 2x2 + x4 = 0 Move the constant term to the right: Add '-0.08695652174' to each side of the equation. 0.08695652174 + 2x2 + -0.08695652174 + x4 = 0 + -0.08695652174 Reorder the terms: 0.08695652174 + -0.08695652174 + 2x2 + x4 = 0 + -0.08695652174 Combine like terms: 0.08695652174 + -0.08695652174 = 0.00000000000 0.00000000000 + 2x2 + x4 = 0 + -0.08695652174 2x2 + x4 = 0 + -0.08695652174 Combine like terms: 0 + -0.08695652174 = -0.08695652174 2x2 + x4 = -0.08695652174 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -0.08695652174 + 1 Reorder the terms: 1 + 2x2 + x4 = -0.08695652174 + 1 Combine like terms: -0.08695652174 + 1 = 0.91304347826 1 + 2x2 + x4 = 0.91304347826 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 0.91304347826 Calculate the square root of the right side: 0.955533086 Break this problem into two subproblems by setting (x2 + 1) equal to 0.955533086 and -0.955533086.Subproblem 1
x2 + 1 = 0.955533086 Simplifying x2 + 1 = 0.955533086 Reorder the terms: 1 + x2 = 0.955533086 Solving 1 + x2 = 0.955533086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0.955533086 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0.955533086 + -1 x2 = 0.955533086 + -1 Combine like terms: 0.955533086 + -1 = -0.044466914 x2 = -0.044466914 Simplifying x2 = -0.044466914 Reorder the terms: 0.044466914 + x2 = -0.044466914 + 0.044466914 Combine like terms: -0.044466914 + 0.044466914 = 0.000000000 0.044466914 + 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 + 1 = -0.955533086 Simplifying x2 + 1 = -0.955533086 Reorder the terms: 1 + x2 = -0.955533086 Solving 1 + x2 = -0.955533086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -0.955533086 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -0.955533086 + -1 x2 = -0.955533086 + -1 Combine like terms: -0.955533086 + -1 = -1.955533086 x2 = -1.955533086 Simplifying x2 = -1.955533086 Reorder the terms: 1.955533086 + x2 = -1.955533086 + 1.955533086 Combine like terms: -1.955533086 + 1.955533086 = 0.000000000 1.955533086 + 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. 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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