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Simplifying 6 + -24x2 + -8x4 = 0 Solving 6 + -24x2 + -8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -12x2 + -4x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -12x2 + -4x4)' equal to zero and attempt to solve: Simplifying 3 + -12x2 + -4x4 = 0 Solving 3 + -12x2 + -4x4 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + 3x2 + x4 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 3x2 + 0.75 + x4 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 3x2 + x4 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 3x2 + x4 = 0 + 0.75 3x2 + x4 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 3x2 + x4 = 0.75 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = 0.75 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 0.75 + 2.25 Combine like terms: 0.75 + 2.25 = 3 2.25 + 3x2 + x4 = 3 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x2 + 1.5) equal to 1.732050808 and -1.732050808.Subproblem 1
x2 + 1.5 = 1.732050808 Simplifying x2 + 1.5 = 1.732050808 Reorder the terms: 1.5 + x2 = 1.732050808 Solving 1.5 + x2 = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 1.732050808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 1.732050808 + -1.5 x2 = 1.732050808 + -1.5 Combine like terms: 1.732050808 + -1.5 = 0.232050808 x2 = 0.232050808 Simplifying x2 = 0.232050808 Take the square root of each side: x = {-0.481716522, 0.481716522}Subproblem 2
x2 + 1.5 = -1.732050808 Simplifying x2 + 1.5 = -1.732050808 Reorder the terms: 1.5 + x2 = -1.732050808 Solving 1.5 + x2 = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -1.732050808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -1.732050808 + -1.5 x2 = -1.732050808 + -1.5 Combine like terms: -1.732050808 + -1.5 = -3.232050808 x2 = -3.232050808 Simplifying x2 = -3.232050808 Reorder the terms: 3.232050808 + x2 = -3.232050808 + 3.232050808 Combine like terms: -3.232050808 + 3.232050808 = 0.000000000 3.232050808 + 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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