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Simplifying x6 + -9x3 + 4 = 0 Reorder the terms: 4 + -9x3 + x6 = 0 Solving 4 + -9x3 + x6 = 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 + -9x3 + -4 + x6 = 0 + -4 Reorder the terms: 4 + -4 + -9x3 + x6 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9x3 + x6 = 0 + -4 -9x3 + x6 = 0 + -4 Combine like terms: 0 + -4 = -4 -9x3 + x6 = -4 The x term is -9x3. 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. -9x3 + 20.25 + x6 = -4 + 20.25 Reorder the terms: 20.25 + -9x3 + x6 = -4 + 20.25 Combine like terms: -4 + 20.25 = 16.25 20.25 + -9x3 + x6 = 16.25 Factor a perfect square on the left side: (x3 + -4.5)(x3 + -4.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x3 + -4.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x3 + -4.5 = 4.031128874 Simplifying x3 + -4.5 = 4.031128874 Reorder the terms: -4.5 + x3 = 4.031128874 Solving -4.5 + x3 = 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 + x3 = 4.031128874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x3 = 4.031128874 + 4.5 x3 = 4.031128874 + 4.5 Combine like terms: 4.031128874 + 4.5 = 8.531128874 x3 = 8.531128874 Simplifying x3 = 8.531128874 Reorder the terms: -8.531128874 + x3 = 8.531128874 + -8.531128874 Combine like terms: 8.531128874 + -8.531128874 = 0.000000000 -8.531128874 + x3 = 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
x3 + -4.5 = -4.031128874 Simplifying x3 + -4.5 = -4.031128874 Reorder the terms: -4.5 + x3 = -4.031128874 Solving -4.5 + x3 = -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 + x3 = -4.031128874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x3 = -4.031128874 + 4.5 x3 = -4.031128874 + 4.5 Combine like terms: -4.031128874 + 4.5 = 0.468871126 x3 = 0.468871126 Simplifying x3 = 0.468871126 Reorder the terms: -0.468871126 + x3 = 0.468871126 + -0.468871126 Combine like terms: 0.468871126 + -0.468871126 = 0.000000000 -0.468871126 + x3 = 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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