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Simplifying x4 + x2 + -720 = 0 Reorder the terms: -720 + x2 + x4 = 0 Solving -720 + x2 + 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 + x2 + 720 + x4 = 0 + 720 Reorder the terms: -720 + 720 + x2 + x4 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + x2 + x4 = 0 + 720 x2 + x4 = 0 + 720 Combine like terms: 0 + 720 = 720 x2 + x4 = 720 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 720 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 720 + 0.25 Combine like terms: 720 + 0.25 = 720.25 0.25 + x2 + x4 = 720.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 720.25 Calculate the square root of the right side: 26.837473801 Break this problem into two subproblems by setting (x2 + 0.5) equal to 26.837473801 and -26.837473801.Subproblem 1
x2 + 0.5 = 26.837473801 Simplifying x2 + 0.5 = 26.837473801 Reorder the terms: 0.5 + x2 = 26.837473801 Solving 0.5 + x2 = 26.837473801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 26.837473801 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 26.837473801 + -0.5 x2 = 26.837473801 + -0.5 Combine like terms: 26.837473801 + -0.5 = 26.337473801 x2 = 26.337473801 Simplifying x2 = 26.337473801 Take the square root of each side: x = {-5.132004852, 5.132004852}Subproblem 2
x2 + 0.5 = -26.837473801 Simplifying x2 + 0.5 = -26.837473801 Reorder the terms: 0.5 + x2 = -26.837473801 Solving 0.5 + x2 = -26.837473801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -26.837473801 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -26.837473801 + -0.5 x2 = -26.837473801 + -0.5 Combine like terms: -26.837473801 + -0.5 = -27.337473801 x2 = -27.337473801 Simplifying x2 = -27.337473801 Reorder the terms: 27.337473801 + x2 = -27.337473801 + 27.337473801 Combine like terms: -27.337473801 + 27.337473801 = 0.000000000 27.337473801 + 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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