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Simplifying 3x6 + -12x4 = 4x2 Reorder the terms: -12x4 + 3x6 = 4x2 Solving -12x4 + 3x6 = 4x2 Solving for variable 'x'. Reorder the terms: -4x2 + -12x4 + 3x6 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4x2 + -12x4 + 3x6 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -12x2 + 3x4) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-4 + -12x2 + 3x4)' equal to zero and attempt to solve: Simplifying -4 + -12x2 + 3x4 = 0 Solving -4 + -12x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -4x2 + x4 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -4x2 + 1.333333333 + x4 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -4x2 + x4 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -4x2 + x4 = 0 + 1.333333333 -4x2 + x4 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -4x2 + x4 = 1.333333333 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 = 1.333333333 + 4 Reorder the terms: 4 + -4x2 + x4 = 1.333333333 + 4 Combine like terms: 1.333333333 + 4 = 5.333333333 4 + -4x2 + x4 = 5.333333333 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (x2 + -2) equal to 2.309401077 and -2.309401077.Subproblem 1
x2 + -2 = 2.309401077 Simplifying x2 + -2 = 2.309401077 Reorder the terms: -2 + x2 = 2.309401077 Solving -2 + x2 = 2.309401077 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 = 2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.309401077 + 2 x2 = 2.309401077 + 2 Combine like terms: 2.309401077 + 2 = 4.309401077 x2 = 4.309401077 Simplifying x2 = 4.309401077 Take the square root of each side: x = {-2.075909699, 2.075909699}Subproblem 2
x2 + -2 = -2.309401077 Simplifying x2 + -2 = -2.309401077 Reorder the terms: -2 + x2 = -2.309401077 Solving -2 + x2 = -2.309401077 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 = -2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.309401077 + 2 x2 = -2.309401077 + 2 Combine like terms: -2.309401077 + 2 = -0.309401077 x2 = -0.309401077 Simplifying x2 = -0.309401077 Reorder the terms: 0.309401077 + x2 = -0.309401077 + 0.309401077 Combine like terms: -0.309401077 + 0.309401077 = 0.000000000 0.309401077 + 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.Solution
x = {0}
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