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Simplifying 2x4 + -16x2 + -18 = 8 Reorder the terms: -18 + -16x2 + 2x4 = 8 Solving -18 + -16x2 + 2x4 = 8 Solving for variable 'x'. Reorder the terms: -18 + -8 + -16x2 + 2x4 = 8 + -8 Combine like terms: -18 + -8 = -26 -26 + -16x2 + 2x4 = 8 + -8 Combine like terms: 8 + -8 = 0 -26 + -16x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -8x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -8x2 + x4)' equal to zero and attempt to solve: Simplifying -13 + -8x2 + x4 = 0 Solving -13 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -8x2 + 13 + x4 = 0 + 13 Reorder the terms: -13 + 13 + -8x2 + x4 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -8x2 + x4 = 0 + 13 -8x2 + x4 = 0 + 13 Combine like terms: 0 + 13 = 13 -8x2 + x4 = 13 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = 13 + 16 Reorder the terms: 16 + -8x2 + x4 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + -8x2 + x4 = 29 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x2 + -4) equal to 5.385164807 and -5.385164807.Subproblem 1
x2 + -4 = 5.385164807 Simplifying x2 + -4 = 5.385164807 Reorder the terms: -4 + x2 = 5.385164807 Solving -4 + x2 = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 5.385164807 + 4 x2 = 5.385164807 + 4 Combine like terms: 5.385164807 + 4 = 9.385164807 x2 = 9.385164807 Simplifying x2 = 9.385164807 Take the square root of each side: x = {-3.063521635, 3.063521635}Subproblem 2
x2 + -4 = -5.385164807 Simplifying x2 + -4 = -5.385164807 Reorder the terms: -4 + x2 = -5.385164807 Solving -4 + x2 = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -5.385164807 + 4 x2 = -5.385164807 + 4 Combine like terms: -5.385164807 + 4 = -1.385164807 x2 = -1.385164807 Simplifying x2 = -1.385164807 Reorder the terms: 1.385164807 + x2 = -1.385164807 + 1.385164807 Combine like terms: -1.385164807 + 1.385164807 = 0.000000000 1.385164807 + 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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