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Simplifying x4 + 19x2 + 72 = 0 Reorder the terms: 72 + 19x2 + x4 = 0 Solving 72 + 19x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + 19x2 + -72 + x4 = 0 + -72 Reorder the terms: 72 + -72 + 19x2 + x4 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + 19x2 + x4 = 0 + -72 19x2 + x4 = 0 + -72 Combine like terms: 0 + -72 = -72 19x2 + x4 = -72 The x term is 19x2. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x2 + 90.25 + x4 = -72 + 90.25 Reorder the terms: 90.25 + 19x2 + x4 = -72 + 90.25 Combine like terms: -72 + 90.25 = 18.25 90.25 + 19x2 + x4 = 18.25 Factor a perfect square on the left side: (x2 + 9.5)(x2 + 9.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x2 + 9.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x2 + 9.5 = 4.272001873 Simplifying x2 + 9.5 = 4.272001873 Reorder the terms: 9.5 + x2 = 4.272001873 Solving 9.5 + x2 = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x2 = 4.272001873 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x2 = 4.272001873 + -9.5 x2 = 4.272001873 + -9.5 Combine like terms: 4.272001873 + -9.5 = -5.227998127 x2 = -5.227998127 Simplifying x2 = -5.227998127 Reorder the terms: 5.227998127 + x2 = -5.227998127 + 5.227998127 Combine like terms: -5.227998127 + 5.227998127 = 0.000000000 5.227998127 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 9.5 = -4.272001873 Simplifying x2 + 9.5 = -4.272001873 Reorder the terms: 9.5 + x2 = -4.272001873 Solving 9.5 + x2 = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x2 = -4.272001873 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x2 = -4.272001873 + -9.5 x2 = -4.272001873 + -9.5 Combine like terms: -4.272001873 + -9.5 = -13.772001873 x2 = -13.772001873 Simplifying x2 = -13.772001873 Reorder the terms: 13.772001873 + x2 = -13.772001873 + 13.772001873 Combine like terms: -13.772001873 + 13.772001873 = 0.000000000 13.772001873 + 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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