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Simplifying x4 + -16x2 + -100 = 0 Reorder the terms: -100 + -16x2 + x4 = 0 Solving -100 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -16x2 + 100 + x4 = 0 + 100 Reorder the terms: -100 + 100 + -16x2 + x4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -16x2 + x4 = 0 + 100 -16x2 + x4 = 0 + 100 Combine like terms: 0 + 100 = 100 -16x2 + x4 = 100 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = 100 + 64 Reorder the terms: 64 + -16x2 + x4 = 100 + 64 Combine like terms: 100 + 64 = 164 64 + -16x2 + x4 = 164 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x2 + -8) equal to 12.806248475 and -12.806248475.Subproblem 1
x2 + -8 = 12.806248475 Simplifying x2 + -8 = 12.806248475 Reorder the terms: -8 + x2 = 12.806248475 Solving -8 + x2 = 12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 12.806248475 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 12.806248475 + 8 x2 = 12.806248475 + 8 Combine like terms: 12.806248475 + 8 = 20.806248475 x2 = 20.806248475 Simplifying x2 = 20.806248475 Take the square root of each side: x = {-4.561386683, 4.561386683}Subproblem 2
x2 + -8 = -12.806248475 Simplifying x2 + -8 = -12.806248475 Reorder the terms: -8 + x2 = -12.806248475 Solving -8 + x2 = -12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -12.806248475 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -12.806248475 + 8 x2 = -12.806248475 + 8 Combine like terms: -12.806248475 + 8 = -4.806248475 x2 = -4.806248475 Simplifying x2 = -4.806248475 Reorder the terms: 4.806248475 + x2 = -4.806248475 + 4.806248475 Combine like terms: -4.806248475 + 4.806248475 = 0.000000000 4.806248475 + 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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