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Simplifying x4 + -8x2 + -80 = 0 Reorder the terms: -80 + -8x2 + x4 = 0 Solving -80 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -8x2 + 80 + x4 = 0 + 80 Reorder the terms: -80 + 80 + -8x2 + x4 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -8x2 + x4 = 0 + 80 -8x2 + x4 = 0 + 80 Combine like terms: 0 + 80 = 80 -8x2 + x4 = 80 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 = 80 + 16 Reorder the terms: 16 + -8x2 + x4 = 80 + 16 Combine like terms: 80 + 16 = 96 16 + -8x2 + x4 = 96 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x2 + -4) equal to 9.797958971 and -9.797958971.Subproblem 1
x2 + -4 = 9.797958971 Simplifying x2 + -4 = 9.797958971 Reorder the terms: -4 + x2 = 9.797958971 Solving -4 + x2 = 9.797958971 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 = 9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 9.797958971 + 4 x2 = 9.797958971 + 4 Combine like terms: 9.797958971 + 4 = 13.797958971 x2 = 13.797958971 Simplifying x2 = 13.797958971 Take the square root of each side: x = {-3.714560401, 3.714560401}Subproblem 2
x2 + -4 = -9.797958971 Simplifying x2 + -4 = -9.797958971 Reorder the terms: -4 + x2 = -9.797958971 Solving -4 + x2 = -9.797958971 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 = -9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -9.797958971 + 4 x2 = -9.797958971 + 4 Combine like terms: -9.797958971 + 4 = -5.797958971 x2 = -5.797958971 Simplifying x2 = -5.797958971 Reorder the terms: 5.797958971 + x2 = -5.797958971 + 5.797958971 Combine like terms: -5.797958971 + 5.797958971 = 0.000000000 5.797958971 + 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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