r^4-7r^2=10

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Solution for r^4-7r^2=10 equation: 


Simplifying
r4 + -7r2 = 10

Reorder the terms:
-7r2 + r4 = 10

Solving
-7r2 + r4 = 10

Solving for variable 'r'.

Reorder the terms:
-10 + -7r2 + r4 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -7r2 + r4 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -7r2 + 10 + r4 = 0 + 10

Reorder the terms:
-10 + 10 + -7r2 + r4 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7r2 + r4 = 0 + 10
-7r2 + r4 = 0 + 10

Combine like terms: 0 + 10 = 10
-7r2 + r4 = 10

The r term is -7r2.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7r2 + 12.25 + r4 = 10 + 12.25

Reorder the terms:
12.25 + -7r2 + r4 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + -7r2 + r4 = 22.25

Factor a perfect square on the left side:
(r2 + -3.5)(r2 + -3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(r2 + -3.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
r2 + -3.5 = 4.716990566

Simplifying
r2 + -3.5 = 4.716990566

Reorder the terms:
-3.5 + r2 = 4.716990566

Solving
-3.5 + r2 = 4.716990566

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + r2 = 4.716990566 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + r2 = 4.716990566 + 3.5
r2 = 4.716990566 + 3.5

Combine like terms: 4.716990566 + 3.5 = 8.216990566
r2 = 8.216990566

Simplifying
r2 = 8.216990566

Take the square root of each side:
r = {-2.866529359, 2.866529359}


Subproblem 2
r2 + -3.5 = -4.716990566

Simplifying
r2 + -3.5 = -4.716990566

Reorder the terms:
-3.5 + r2 = -4.716990566

Solving
-3.5 + r2 = -4.716990566

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + r2 = -4.716990566 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + r2 = -4.716990566 + 3.5
r2 = -4.716990566 + 3.5

Combine like terms: -4.716990566 + 3.5 = -1.216990566
r2 = -1.216990566

Simplifying
r2 = -1.216990566

Reorder the terms:
1.216990566 + r2 = -1.216990566 + 1.216990566

Combine like terms: -1.216990566 + 1.216990566 = 0.000000000
1.216990566 + 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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