r^4-10r^2-9=0

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Solution for r^4-10r^2-9=0 equation:


Simplifying
r4 + -10r2 + -9 = 0

Reorder the terms:
-9 + -10r2 + r4 = 0

Solving
-9 + -10r2 + r4 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -10r2 + 9 + r4 = 0 + 9

Reorder the terms:
-9 + 9 + -10r2 + r4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -10r2 + r4 = 0 + 9
-10r2 + r4 = 0 + 9

Combine like terms: 0 + 9 = 9
-10r2 + r4 = 9

The r term is -10r2.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r2 + 25 + r4 = 9 + 25

Reorder the terms:
25 + -10r2 + r4 = 9 + 25

Combine like terms: 9 + 25 = 34
25 + -10r2 + r4 = 34

Factor a perfect square on the left side:
(r2 + -5)(r2 + -5) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(r2 + -5) equal to 5.830951895 and -5.830951895.

Subproblem 1

r2 + -5 = 5.830951895 Simplifying r2 + -5 = 5.830951895 Reorder the terms: -5 + r2 = 5.830951895 Solving -5 + r2 = 5.830951895 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r2 = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + r2 = 5.830951895 + 5 r2 = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 r2 = 10.830951895 Simplifying r2 = 10.830951895 Take the square root of each side: r = {-3.291041157, 3.291041157}

Subproblem 2

r2 + -5 = -5.830951895 Simplifying r2 + -5 = -5.830951895 Reorder the terms: -5 + r2 = -5.830951895 Solving -5 + r2 = -5.830951895 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r2 = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + r2 = -5.830951895 + 5 r2 = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 r2 = -0.830951895 Simplifying r2 = -0.830951895 Reorder the terms: 0.830951895 + r2 = -0.830951895 + 0.830951895 Combine like terms: -0.830951895 + 0.830951895 = 0.000000000 0.830951895 + 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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