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Simplifying r4 + 15r2 + -18 = 0 Reorder the terms: -18 + 15r2 + r4 = 0 Solving -18 + 15r2 + 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 + 15r2 + 18 + r4 = 0 + 18 Reorder the terms: -18 + 18 + 15r2 + r4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 15r2 + r4 = 0 + 18 15r2 + r4 = 0 + 18 Combine like terms: 0 + 18 = 18 15r2 + r4 = 18 The r term is 15r2. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15r2 + 56.25 + r4 = 18 + 56.25 Reorder the terms: 56.25 + 15r2 + r4 = 18 + 56.25 Combine like terms: 18 + 56.25 = 74.25 56.25 + 15r2 + r4 = 74.25 Factor a perfect square on the left side: (r2 + 7.5)(r2 + 7.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (r2 + 7.5) equal to 8.61684397 and -8.61684397.Subproblem 1
r2 + 7.5 = 8.61684397 Simplifying r2 + 7.5 = 8.61684397 Reorder the terms: 7.5 + r2 = 8.61684397 Solving 7.5 + r2 = 8.61684397 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r2 = 8.61684397 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r2 = 8.61684397 + -7.5 r2 = 8.61684397 + -7.5 Combine like terms: 8.61684397 + -7.5 = 1.11684397 r2 = 1.11684397 Simplifying r2 = 1.11684397 Take the square root of each side: r = {-1.056808388, 1.056808388}Subproblem 2
r2 + 7.5 = -8.61684397 Simplifying r2 + 7.5 = -8.61684397 Reorder the terms: 7.5 + r2 = -8.61684397 Solving 7.5 + r2 = -8.61684397 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r2 = -8.61684397 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r2 = -8.61684397 + -7.5 r2 = -8.61684397 + -7.5 Combine like terms: -8.61684397 + -7.5 = -16.11684397 r2 = -16.11684397 Simplifying r2 = -16.11684397 Reorder the terms: 16.11684397 + r2 = -16.11684397 + 16.11684397 Combine like terms: -16.11684397 + 16.11684397 = 0.00000000 16.11684397 + r2 = 0.00000000 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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