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Simplifying 3x4 + 12x2 + -5 = 0 Reorder the terms: -5 + 12x2 + 3x4 = 0 Solving -5 + 12x2 + 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'. -1.666666667 + 4x2 + x4 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 4x2 + 1.666666667 + x4 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 4x2 + x4 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 4x2 + x4 = 0 + 1.666666667 4x2 + x4 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 4x2 + x4 = 1.666666667 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 1.666666667 + 4 Reorder the terms: 4 + 4x2 + x4 = 1.666666667 + 4 Combine like terms: 1.666666667 + 4 = 5.666666667 4 + 4x2 + x4 = 5.666666667 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x2 + 2) equal to 2.380476143 and -2.380476143.Subproblem 1
x2 + 2 = 2.380476143 Simplifying x2 + 2 = 2.380476143 Reorder the terms: 2 + x2 = 2.380476143 Solving 2 + x2 = 2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 2.380476143 + -2 x2 = 2.380476143 + -2 Combine like terms: 2.380476143 + -2 = 0.380476143 x2 = 0.380476143 Simplifying x2 = 0.380476143 Take the square root of each side: x = {-0.616827482, 0.616827482}Subproblem 2
x2 + 2 = -2.380476143 Simplifying x2 + 2 = -2.380476143 Reorder the terms: 2 + x2 = -2.380476143 Solving 2 + x2 = -2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -2.380476143 + -2 x2 = -2.380476143 + -2 Combine like terms: -2.380476143 + -2 = -4.380476143 x2 = -4.380476143 Simplifying x2 = -4.380476143 Reorder the terms: 4.380476143 + x2 = -4.380476143 + 4.380476143 Combine like terms: -4.380476143 + 4.380476143 = 0.000000000 4.380476143 + 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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