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Simplifying x4 + 2x2 + -59 = 0 Reorder the terms: -59 + 2x2 + x4 = 0 Solving -59 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 2x2 + 59 + x4 = 0 + 59 Reorder the terms: -59 + 59 + 2x2 + x4 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 2x2 + x4 = 0 + 59 2x2 + x4 = 0 + 59 Combine like terms: 0 + 59 = 59 2x2 + x4 = 59 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 59 + 1 Reorder the terms: 1 + 2x2 + x4 = 59 + 1 Combine like terms: 59 + 1 = 60 1 + 2x2 + x4 = 60 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x2 + 1) equal to 7.745966692 and -7.745966692.Subproblem 1
x2 + 1 = 7.745966692 Simplifying x2 + 1 = 7.745966692 Reorder the terms: 1 + x2 = 7.745966692 Solving 1 + x2 = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 7.745966692 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 7.745966692 + -1 x2 = 7.745966692 + -1 Combine like terms: 7.745966692 + -1 = 6.745966692 x2 = 6.745966692 Simplifying x2 = 6.745966692 Take the square root of each side: x = {-2.597299885, 2.597299885}Subproblem 2
x2 + 1 = -7.745966692 Simplifying x2 + 1 = -7.745966692 Reorder the terms: 1 + x2 = -7.745966692 Solving 1 + x2 = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -7.745966692 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -7.745966692 + -1 x2 = -7.745966692 + -1 Combine like terms: -7.745966692 + -1 = -8.745966692 x2 = -8.745966692 Simplifying x2 = -8.745966692 Reorder the terms: 8.745966692 + x2 = -8.745966692 + 8.745966692 Combine like terms: -8.745966692 + 8.745966692 = 0.000000000 8.745966692 + 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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