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Simplifying r4 + r2 + -18 = 0 Reorder the terms: -18 + r2 + r4 = 0 Solving -18 + r2 + r4 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + r2 + 18 + r4 = 0 + 18 Reorder the terms: -18 + 18 + r2 + r4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + r2 + r4 = 0 + 18 r2 + r4 = 0 + 18 Combine like terms: 0 + 18 = 18 r2 + r4 = 18 The r term is r2. 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. r2 + 0.25 + r4 = 18 + 0.25 Reorder the terms: 0.25 + r2 + r4 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + r2 + r4 = 18.25 Factor a perfect square on the left side: (r2 + 0.5)(r2 + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (r2 + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
r2 + 0.5 = 4.272001873 Simplifying r2 + 0.5 = 4.272001873 Reorder the terms: 0.5 + r2 = 4.272001873 Solving 0.5 + r2 = 4.272001873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r2 = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r2 = 4.272001873 + -0.5 r2 = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 r2 = 3.772001873 Simplifying r2 = 3.772001873 Take the square root of each side: r = {-1.942164224, 1.942164224}Subproblem 2
r2 + 0.5 = -4.272001873 Simplifying r2 + 0.5 = -4.272001873 Reorder the terms: 0.5 + r2 = -4.272001873 Solving 0.5 + r2 = -4.272001873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r2 = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r2 = -4.272001873 + -0.5 r2 = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 r2 = -4.772001873 Simplifying r2 = -4.772001873 Reorder the terms: 4.772001873 + r2 = -4.772001873 + 4.772001873 Combine like terms: -4.772001873 + 4.772001873 = 0.000000000 4.772001873 + r2 = 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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