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Simplifying x4 + 2x2 + -720 = 0 Reorder the terms: -720 + 2x2 + x4 = 0 Solving -720 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '720' to each side of the equation. -720 + 2x2 + 720 + x4 = 0 + 720 Reorder the terms: -720 + 720 + 2x2 + x4 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + 2x2 + x4 = 0 + 720 2x2 + x4 = 0 + 720 Combine like terms: 0 + 720 = 720 2x2 + x4 = 720 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 = 720 + 1 Reorder the terms: 1 + 2x2 + x4 = 720 + 1 Combine like terms: 720 + 1 = 721 1 + 2x2 + x4 = 721 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 721 Calculate the square root of the right side: 26.851443164 Break this problem into two subproblems by setting (x2 + 1) equal to 26.851443164 and -26.851443164.Subproblem 1
x2 + 1 = 26.851443164 Simplifying x2 + 1 = 26.851443164 Reorder the terms: 1 + x2 = 26.851443164 Solving 1 + x2 = 26.851443164 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 = 26.851443164 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 26.851443164 + -1 x2 = 26.851443164 + -1 Combine like terms: 26.851443164 + -1 = 25.851443164 x2 = 25.851443164 Simplifying x2 = 25.851443164 Take the square root of each side: x = {-5.084431449, 5.084431449}Subproblem 2
x2 + 1 = -26.851443164 Simplifying x2 + 1 = -26.851443164 Reorder the terms: 1 + x2 = -26.851443164 Solving 1 + x2 = -26.851443164 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 = -26.851443164 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -26.851443164 + -1 x2 = -26.851443164 + -1 Combine like terms: -26.851443164 + -1 = -27.851443164 x2 = -27.851443164 Simplifying x2 = -27.851443164 Reorder the terms: 27.851443164 + x2 = -27.851443164 + 27.851443164 Combine like terms: -27.851443164 + 27.851443164 = 0.000000000 27.851443164 + 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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