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Simplifying 0 = x4 + -27x2 + -8 Reorder the terms: 0 = -8 + -27x2 + x4 Solving 0 = -8 + -27x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + 27x2 + -1x4 = -8 + -27x2 + x4 + 8 + 27x2 + -1x4 Reorder the terms: 8 + 27x2 + -1x4 = -8 + 8 + -27x2 + 27x2 + x4 + -1x4 Combine like terms: -8 + 8 = 0 8 + 27x2 + -1x4 = 0 + -27x2 + 27x2 + x4 + -1x4 8 + 27x2 + -1x4 = -27x2 + 27x2 + x4 + -1x4 Combine like terms: -27x2 + 27x2 = 0 8 + 27x2 + -1x4 = 0 + x4 + -1x4 8 + 27x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 8 + 27x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -27x2 + x4 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -27x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + -27x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -27x2 + x4 = 0 + 8 -27x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 -27x2 + x4 = 8 The x term is -27x2. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x2 + 182.25 + x4 = 8 + 182.25 Reorder the terms: 182.25 + -27x2 + x4 = 8 + 182.25 Combine like terms: 8 + 182.25 = 190.25 182.25 + -27x2 + x4 = 190.25 Factor a perfect square on the left side: (x2 + -13.5)(x2 + -13.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x2 + -13.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x2 + -13.5 = 13.793114224 Simplifying x2 + -13.5 = 13.793114224 Reorder the terms: -13.5 + x2 = 13.793114224 Solving -13.5 + x2 = 13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x2 = 13.793114224 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x2 = 13.793114224 + 13.5 x2 = 13.793114224 + 13.5 Combine like terms: 13.793114224 + 13.5 = 27.293114224 x2 = 27.293114224 Simplifying x2 = 27.293114224 Take the square root of each side: x = {-5.224281216, 5.224281216}Subproblem 2
x2 + -13.5 = -13.793114224 Simplifying x2 + -13.5 = -13.793114224 Reorder the terms: -13.5 + x2 = -13.793114224 Solving -13.5 + x2 = -13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x2 = -13.793114224 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x2 = -13.793114224 + 13.5 x2 = -13.793114224 + 13.5 Combine like terms: -13.793114224 + 13.5 = -0.293114224 x2 = -0.293114224 Simplifying x2 = -0.293114224 Reorder the terms: 0.293114224 + x2 = -0.293114224 + 0.293114224 Combine like terms: -0.293114224 + 0.293114224 = 0.000000000 0.293114224 + 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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