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Simplifying x4 + -8x2 + -72 = 0 Reorder the terms: -72 + -8x2 + x4 = 0 Solving -72 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -8x2 + 72 + x4 = 0 + 72 Reorder the terms: -72 + 72 + -8x2 + x4 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -8x2 + x4 = 0 + 72 -8x2 + x4 = 0 + 72 Combine like terms: 0 + 72 = 72 -8x2 + x4 = 72 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 = 72 + 16 Reorder the terms: 16 + -8x2 + x4 = 72 + 16 Combine like terms: 72 + 16 = 88 16 + -8x2 + x4 = 88 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x2 + -4) equal to 9.38083152 and -9.38083152.Subproblem 1
x2 + -4 = 9.38083152 Simplifying x2 + -4 = 9.38083152 Reorder the terms: -4 + x2 = 9.38083152 Solving -4 + x2 = 9.38083152 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 = 9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 9.38083152 + 4 x2 = 9.38083152 + 4 Combine like terms: 9.38083152 + 4 = 13.38083152 x2 = 13.38083152 Simplifying x2 = 13.38083152 Take the square root of each side: x = {-3.657981892, 3.657981892}Subproblem 2
x2 + -4 = -9.38083152 Simplifying x2 + -4 = -9.38083152 Reorder the terms: -4 + x2 = -9.38083152 Solving -4 + x2 = -9.38083152 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 = -9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -9.38083152 + 4 x2 = -9.38083152 + 4 Combine like terms: -9.38083152 + 4 = -5.38083152 x2 = -5.38083152 Simplifying x2 = -5.38083152 Reorder the terms: 5.38083152 + x2 = -5.38083152 + 5.38083152 Combine like terms: -5.38083152 + 5.38083152 = 0.00000000 5.38083152 + x2 = 0.00000000 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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