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Simplifying 0.0000000000005x4 + 0.5x2 + -0.5 = 0 Reorder the terms: -0.5 + 0.5x2 + 0.0000000000005x4 = 0 Solving -0.5 + 0.5x2 + 0.0000000000005x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0000000000005 the coefficient of the squared term: Divide each side by '0.0000000000005'. -1000000000000 + 1000000000000x2 + x4 = 0 Move the constant term to the right: Add '1000000000000' to each side of the equation. -1000000000000 + 1000000000000x2 + 1000000000000 + x4 = 0 + 1000000000000 Reorder the terms: -1000000000000 + 1000000000000 + 1000000000000x2 + x4 = 0 + 1000000000000 Combine like terms: -1000000000000 + 1000000000000 = 0 0 + 1000000000000x2 + x4 = 0 + 1000000000000 1000000000000x2 + x4 = 0 + 1000000000000 Combine like terms: 0 + 1000000000000 = 1000000000000 1000000000000x2 + x4 = 1000000000000 The x term is 1000000000000x2. Take half its coefficient (500000000000). Square it (250000000000000000000000) and add it to both sides. Add '250000000000000000000000' to each side of the equation. 1000000000000x2 + 250000000000000000000000 + x4 = 1000000000000 + 250000000000000000000000 Reorder the terms: 250000000000000000000000 + 1000000000000x2 + x4 = 1000000000000 + 250000000000000000000000 Combine like terms: 1000000000000 + 250000000000000000000000 = 250000000001000000000000 250000000000000000000000 + 1000000000000x2 + x4 = 250000000001000000000000 Factor a perfect square on the left side: (x2 + 500000000000)(x2 + 500000000000) = 250000000001000000000000 Calculate the square root of the right side: 500000000001 Break this problem into two subproblems by setting (x2 + 500000000000) equal to 500000000001 and -500000000001.Subproblem 1
x2 + 500000000000 = 500000000001 Simplifying x2 + 500000000000 = 500000000001 Reorder the terms: 500000000000 + x2 = 500000000001 Solving 500000000000 + x2 = 500000000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-500000000000' to each side of the equation. 500000000000 + -500000000000 + x2 = 500000000001 + -500000000000 Combine like terms: 500000000000 + -500000000000 = 0 0 + x2 = 500000000001 + -500000000000 x2 = 500000000001 + -500000000000 Combine like terms: 500000000001 + -500000000000 = 1 x2 = 1 Simplifying x2 = 1 Take the square root of each side: x = {-1, 1}Subproblem 2
x2 + 500000000000 = -500000000001 Simplifying x2 + 500000000000 = -500000000001 Reorder the terms: 500000000000 + x2 = -500000000001 Solving 500000000000 + x2 = -500000000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-500000000000' to each side of the equation. 500000000000 + -500000000000 + x2 = -500000000001 + -500000000000 Combine like terms: 500000000000 + -500000000000 = 0 0 + x2 = -500000000001 + -500000000000 x2 = -500000000001 + -500000000000 Combine like terms: -500000000001 + -500000000000 = -1000000000001 x2 = -1000000000001 Simplifying x2 = -1000000000001 Reorder the terms: 1000000000001 + x2 = -1000000000001 + 1000000000001 Combine like terms: -1000000000001 + 1000000000001 = 0 1000000000001 + x2 = 0 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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