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Simplifying 108x4 + -432x2 + -384 = 0 Reorder the terms: -384 + -432x2 + 108x4 = 0 Solving -384 + -432x2 + 108x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-32 + -36x2 + 9x4) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-32 + -36x2 + 9x4)' equal to zero and attempt to solve: Simplifying -32 + -36x2 + 9x4 = 0 Solving -32 + -36x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.555555556 + -4x2 + x4 = 0 Move the constant term to the right: Add '3.555555556' to each side of the equation. -3.555555556 + -4x2 + 3.555555556 + x4 = 0 + 3.555555556 Reorder the terms: -3.555555556 + 3.555555556 + -4x2 + x4 = 0 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + -4x2 + x4 = 0 + 3.555555556 -4x2 + x4 = 0 + 3.555555556 Combine like terms: 0 + 3.555555556 = 3.555555556 -4x2 + x4 = 3.555555556 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 = 3.555555556 + 4 Reorder the terms: 4 + -4x2 + x4 = 3.555555556 + 4 Combine like terms: 3.555555556 + 4 = 7.555555556 4 + -4x2 + x4 = 7.555555556 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 7.555555556 Calculate the square root of the right side: 2.748737084 Break this problem into two subproblems by setting (x2 + -2) equal to 2.748737084 and -2.748737084.Subproblem 1
x2 + -2 = 2.748737084 Simplifying x2 + -2 = 2.748737084 Reorder the terms: -2 + x2 = 2.748737084 Solving -2 + x2 = 2.748737084 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 = 2.748737084 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.748737084 + 2 x2 = 2.748737084 + 2 Combine like terms: 2.748737084 + 2 = 4.748737084 x2 = 4.748737084 Simplifying x2 = 4.748737084 Take the square root of each side: x = {-2.17915972, 2.17915972}Subproblem 2
x2 + -2 = -2.748737084 Simplifying x2 + -2 = -2.748737084 Reorder the terms: -2 + x2 = -2.748737084 Solving -2 + x2 = -2.748737084 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 = -2.748737084 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.748737084 + 2 x2 = -2.748737084 + 2 Combine like terms: -2.748737084 + 2 = -0.748737084 x2 = -0.748737084 Simplifying x2 = -0.748737084 Reorder the terms: 0.748737084 + x2 = -0.748737084 + 0.748737084 Combine like terms: -0.748737084 + 0.748737084 = 0.000000000 0.748737084 + 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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