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Simplifying x4 + -5x2 + -8 = 0 Reorder the terms: -8 + -5x2 + x4 = 0 Solving -8 + -5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -5x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + -5x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5x2 + x4 = 0 + 8 -5x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 -5x2 + x4 = 8 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = 8 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + -5x2 + x4 = 14.25 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x2 + -2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x2 + -2.5 = 3.774917218 Simplifying x2 + -2.5 = 3.774917218 Reorder the terms: -2.5 + x2 = 3.774917218 Solving -2.5 + x2 = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 3.774917218 + 2.5 x2 = 3.774917218 + 2.5 Combine like terms: 3.774917218 + 2.5 = 6.274917218 x2 = 6.274917218 Simplifying x2 = 6.274917218 Take the square root of each side: x = {-2.504978487, 2.504978487}Subproblem 2
x2 + -2.5 = -3.774917218 Simplifying x2 + -2.5 = -3.774917218 Reorder the terms: -2.5 + x2 = -3.774917218 Solving -2.5 + x2 = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -3.774917218 + 2.5 x2 = -3.774917218 + 2.5 Combine like terms: -3.774917218 + 2.5 = -1.274917218 x2 = -1.274917218 Simplifying x2 = -1.274917218 Reorder the terms: 1.274917218 + x2 = -1.274917218 + 1.274917218 Combine like terms: -1.274917218 + 1.274917218 = 0.000000000 1.274917218 + 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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