t^2(t^2-5)=2t^2-5

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Solution for t^2(t^2-5)=2t^2-5 equation: 


Simplifying
t2(t2 + -5) = 2t2 + -5

Reorder the terms:
t2(-5 + t2) = 2t2 + -5
(-5 * t2 + t2 * t2) = 2t2 + -5
(-5t2 + t4) = 2t2 + -5

Reorder the terms:
-5t2 + t4 = -5 + 2t2

Solving
-5t2 + t4 = -5 + 2t2

Solving for variable 't'.

Reorder the terms:
5 + -5t2 + -2t2 + t4 = -5 + 2t2 + 5 + -2t2

Combine like terms: -5t2 + -2t2 = -7t2
5 + -7t2 + t4 = -5 + 2t2 + 5 + -2t2

Reorder the terms:
5 + -7t2 + t4 = -5 + 5 + 2t2 + -2t2

Combine like terms: -5 + 5 = 0
5 + -7t2 + t4 = 0 + 2t2 + -2t2
5 + -7t2 + t4 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
5 + -7t2 + t4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -7t2 + -5 + t4 = 0 + -5

Reorder the terms:
5 + -5 + -7t2 + t4 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7t2 + t4 = 0 + -5
-7t2 + t4 = 0 + -5

Combine like terms: 0 + -5 = -5
-7t2 + t4 = -5

The t term is -7t2.  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.
-7t2 + 12.25 + t4 = -5 + 12.25

Reorder the terms:
12.25 + -7t2 + t4 = -5 + 12.25

Combine like terms: -5 + 12.25 = 7.25
12.25 + -7t2 + t4 = 7.25

Factor a perfect square on the left side:
(t2 + -3.5)(t2 + -3.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(t2 + -3.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
t2 + -3.5 = 2.692582404

Simplifying
t2 + -3.5 = 2.692582404

Reorder the terms:
-3.5 + t2 = 2.692582404

Solving
-3.5 + t2 = 2.692582404

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t2 = 2.692582404 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t2 = 2.692582404 + 3.5
t2 = 2.692582404 + 3.5

Combine like terms: 2.692582404 + 3.5 = 6.192582404
t2 = 6.192582404

Simplifying
t2 = 6.192582404

Take the square root of each side:
t = {-2.488489985, 2.488489985}


Subproblem 2
t2 + -3.5 = -2.692582404

Simplifying
t2 + -3.5 = -2.692582404

Reorder the terms:
-3.5 + t2 = -2.692582404

Solving
-3.5 + t2 = -2.692582404

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t2 = -2.692582404 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t2 = -2.692582404 + 3.5
t2 = -2.692582404 + 3.5

Combine like terms: -2.692582404 + 3.5 = 0.807417596
t2 = 0.807417596

Simplifying
t2 = 0.807417596

Take the square root of each side:
t = {-0.898564186, 0.898564186}


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-2.488489985, 2.488489985, -0.898564186, 0.898564186}

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