r^4+15r^2-18=0

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Solution for r^4+15r^2-18=0 equation:


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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