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Simplifying x4 + 100x2 + -100 = 0 Reorder the terms: -100 + 100x2 + x4 = 0 Solving -100 + 100x2 + 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 + 100x2 + 100 + x4 = 0 + 100 Reorder the terms: -100 + 100 + 100x2 + x4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 100x2 + x4 = 0 + 100 100x2 + x4 = 0 + 100 Combine like terms: 0 + 100 = 100 100x2 + x4 = 100 The x term is 100x2. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x2 + 2500 + x4 = 100 + 2500 Reorder the terms: 2500 + 100x2 + x4 = 100 + 2500 Combine like terms: 100 + 2500 = 2600 2500 + 100x2 + x4 = 2600 Factor a perfect square on the left side: (x2 + 50)(x2 + 50) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (x2 + 50) equal to 50.990195136 and -50.990195136.Subproblem 1
x2 + 50 = 50.990195136 Simplifying x2 + 50 = 50.990195136 Reorder the terms: 50 + x2 = 50.990195136 Solving 50 + x2 = 50.990195136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x2 = 50.990195136 + -50 Combine like terms: 50 + -50 = 0 0 + x2 = 50.990195136 + -50 x2 = 50.990195136 + -50 Combine like terms: 50.990195136 + -50 = 0.990195136 x2 = 0.990195136 Simplifying x2 = 0.990195136 Take the square root of each side: x = {-0.995085492, 0.995085492}Subproblem 2
x2 + 50 = -50.990195136 Simplifying x2 + 50 = -50.990195136 Reorder the terms: 50 + x2 = -50.990195136 Solving 50 + x2 = -50.990195136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x2 = -50.990195136 + -50 Combine like terms: 50 + -50 = 0 0 + x2 = -50.990195136 + -50 x2 = -50.990195136 + -50 Combine like terms: -50.990195136 + -50 = -100.990195136 x2 = -100.990195136 Simplifying x2 = -100.990195136 Reorder the terms: 100.990195136 + x2 = -100.990195136 + 100.990195136 Combine like terms: -100.990195136 + 100.990195136 = 0.000000000 100.990195136 + 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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