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Simplifying x4 + 9x2 + 4 = 0 Reorder the terms: 4 + 9x2 + x4 = 0 Solving 4 + 9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 9x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + 9x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9x2 + x4 = 0 + -4 9x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 9x2 + x4 = -4 The x term is 9x2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x2 + 20.25 + x4 = -4 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = -4 + 20.25 Combine like terms: -4 + 20.25 = 16.25 20.25 + 9x2 + x4 = 16.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x2 + 4.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x2 + 4.5 = 4.031128874 Simplifying x2 + 4.5 = 4.031128874 Reorder the terms: 4.5 + x2 = 4.031128874 Solving 4.5 + x2 = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 4.031128874 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 4.031128874 + -4.5 x2 = 4.031128874 + -4.5 Combine like terms: 4.031128874 + -4.5 = -0.468871126 x2 = -0.468871126 Simplifying x2 = -0.468871126 Reorder the terms: 0.468871126 + x2 = -0.468871126 + 0.468871126 Combine like terms: -0.468871126 + 0.468871126 = 0.000000000 0.468871126 + 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 + 4.5 = -4.031128874 Simplifying x2 + 4.5 = -4.031128874 Reorder the terms: 4.5 + x2 = -4.031128874 Solving 4.5 + x2 = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -4.031128874 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -4.031128874 + -4.5 x2 = -4.031128874 + -4.5 Combine like terms: -4.031128874 + -4.5 = -8.531128874 x2 = -8.531128874 Simplifying x2 = -8.531128874 Reorder the terms: 8.531128874 + x2 = -8.531128874 + 8.531128874 Combine like terms: -8.531128874 + 8.531128874 = 0.000000000 8.531128874 + 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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