225=10.76t^2+.92t^4

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Solution for 225=10.76t^2+.92t^4 equation: 


Simplifying
225 = 10.76t2 + 0.92t4

Solving
225 = 10.76t2 + 0.92t4

Solving for variable 't'.

Reorder the terms:
225 + -10.76t2 + -0.92t4 = 10.76t2 + -10.76t2 + 0.92t4 + -0.92t4

Combine like terms: 10.76t2 + -10.76t2 = 0.00
225 + -10.76t2 + -0.92t4 = 0.00 + 0.92t4 + -0.92t4
225 + -10.76t2 + -0.92t4 = 0.92t4 + -0.92t4

Combine like terms: 0.92t4 + -0.92t4 = 0.00
225 + -10.76t2 + -0.92t4 = 0.00

Begin completing the square.  Divide all terms by
-0.92 the coefficient of the squared term: 

Divide each side by '-0.92'.
-244.5652174 + 11.69565217t2 + t4 = 0

Move the constant term to the right:

Add '244.5652174' to each side of the equation.
-244.5652174 + 11.69565217t2 + 244.5652174 + t4 = 0 + 244.5652174

Reorder the terms:
-244.5652174 + 244.5652174 + 11.69565217t2 + t4 = 0 + 244.5652174

Combine like terms: -244.5652174 + 244.5652174 = 0.0000000
0.0000000 + 11.69565217t2 + t4 = 0 + 244.5652174
11.69565217t2 + t4 = 0 + 244.5652174

Combine like terms: 0 + 244.5652174 = 244.5652174
11.69565217t2 + t4 = 244.5652174

The t term is 11.69565217t2.  Take half its coefficient (5.847826085).
Square it (34.19706992) and add it to both sides.

Add '34.19706992' to each side of the equation.
11.69565217t2 + 34.19706992 + t4 = 244.5652174 + 34.19706992

Reorder the terms:
34.19706992 + 11.69565217t2 + t4 = 244.5652174 + 34.19706992

Combine like terms: 244.5652174 + 34.19706992 = 278.76228732
34.19706992 + 11.69565217t2 + t4 = 278.76228732

Factor a perfect square on the left side:
(t2 + 5.847826085)(t2 + 5.847826085) = 278.76228732

Calculate the square root of the right side: 16.696175829

Break this problem into two subproblems by setting 
(t2 + 5.847826085) equal to 16.696175829 and -16.696175829.


Subproblem 1
t2 + 5.847826085 = 16.696175829

Simplifying
t2 + 5.847826085 = 16.696175829

Reorder the terms:
5.847826085 + t2 = 16.696175829

Solving
5.847826085 + t2 = 16.696175829

Solving for variable 't'.

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

Add '-5.847826085' to each side of the equation.
5.847826085 + -5.847826085 + t2 = 16.696175829 + -5.847826085

Combine like terms: 5.847826085 + -5.847826085 = 0.000000000
0.000000000 + t2 = 16.696175829 + -5.847826085
t2 = 16.696175829 + -5.847826085

Combine like terms: 16.696175829 + -5.847826085 = 10.848349744
t2 = 10.848349744

Simplifying
t2 = 10.848349744

Take the square root of each side:
t = {-3.29368331, 3.29368331}


Subproblem 2
t2 + 5.847826085 = -16.696175829

Simplifying
t2 + 5.847826085 = -16.696175829

Reorder the terms:
5.847826085 + t2 = -16.696175829

Solving
5.847826085 + t2 = -16.696175829

Solving for variable 't'.

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

Add '-5.847826085' to each side of the equation.
5.847826085 + -5.847826085 + t2 = -16.696175829 + -5.847826085

Combine like terms: 5.847826085 + -5.847826085 = 0.000000000
0.000000000 + t2 = -16.696175829 + -5.847826085
t2 = -16.696175829 + -5.847826085

Combine like terms: -16.696175829 + -5.847826085 = -22.544001914
t2 = -22.544001914

Simplifying
t2 = -22.544001914

Reorder the terms:
22.544001914 + t2 = -22.544001914 + 22.544001914

Combine like terms: -22.544001914 + 22.544001914 = 0.000000000
22.544001914 + t2 = 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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