12t^4+19t^2-144=0

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Solution for 12t^4+19t^2-144=0 equation:


Simplifying
12t4 + 19t2 + -144 = 0

Reorder the terms:
-144 + 19t2 + 12t4 = 0

Solving
-144 + 19t2 + 12t4 = 0

Solving for variable 't'.

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

Divide each side by '12'.
-12 + 1.583333333t2 + t4 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 1.583333333t2 + 12 + t4 = 0 + 12

Reorder the terms:
-12 + 12 + 1.583333333t2 + t4 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 1.583333333t2 + t4 = 0 + 12
1.583333333t2 + t4 = 0 + 12

Combine like terms: 0 + 12 = 12
1.583333333t2 + t4 = 12

The t term is 1.583333333t2.  Take half its coefficient (0.7916666665).
Square it (0.6267361108) and add it to both sides.

Add '0.6267361108' to each side of the equation.
1.583333333t2 + 0.6267361108 + t4 = 12 + 0.6267361108

Reorder the terms:
0.6267361108 + 1.583333333t2 + t4 = 12 + 0.6267361108

Combine like terms: 12 + 0.6267361108 = 12.6267361108
0.6267361108 + 1.583333333t2 + t4 = 12.6267361108

Factor a perfect square on the left side:
(t2 + 0.7916666665)(t2 + 0.7916666665) = 12.6267361108

Calculate the square root of the right side: 3.553411897

Break this problem into two subproblems by setting 
(t2 + 0.7916666665) equal to 3.553411897 and -3.553411897.

Subproblem 1

t2 + 0.7916666665 = 3.553411897 Simplifying t2 + 0.7916666665 = 3.553411897 Reorder the terms: 0.7916666665 + t2 = 3.553411897 Solving 0.7916666665 + t2 = 3.553411897 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + t2 = 3.553411897 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + t2 = 3.553411897 + -0.7916666665 t2 = 3.553411897 + -0.7916666665 Combine like terms: 3.553411897 + -0.7916666665 = 2.7617452305 t2 = 2.7617452305 Simplifying t2 = 2.7617452305 Take the square root of each side: t = {-1.661849942, 1.661849942}

Subproblem 2

t2 + 0.7916666665 = -3.553411897 Simplifying t2 + 0.7916666665 = -3.553411897 Reorder the terms: 0.7916666665 + t2 = -3.553411897 Solving 0.7916666665 + t2 = -3.553411897 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + t2 = -3.553411897 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + t2 = -3.553411897 + -0.7916666665 t2 = -3.553411897 + -0.7916666665 Combine like terms: -3.553411897 + -0.7916666665 = -4.3450785635 t2 = -4.3450785635 Simplifying t2 = -4.3450785635 Reorder the terms: 4.3450785635 + t2 = -4.3450785635 + 4.3450785635 Combine like terms: -4.3450785635 + 4.3450785635 = 0.0000000000 4.3450785635 + t2 = 0.0000000000 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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