8t^4+5t^2-4=0

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Solution for 8t^4+5t^2-4=0 equation:


Simplifying
8t4 + 5t2 + -4 = 0

Reorder the terms:
-4 + 5t2 + 8t4 = 0

Solving
-4 + 5t2 + 8t4 = 0

Solving for variable 't'.

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

Divide each side by '8'.
-0.5 + 0.625t2 + t4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.625t2 + 0.5 + t4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.625t2 + t4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.625t2 + t4 = 0 + 0.5
0.625t2 + t4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.625t2 + t4 = 0.5

The t term is 0.625t2.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625t2 + 0.09765625 + t4 = 0.5 + 0.09765625

Reorder the terms:
0.09765625 + 0.625t2 + t4 = 0.5 + 0.09765625

Combine like terms: 0.5 + 0.09765625 = 0.59765625
0.09765625 + 0.625t2 + t4 = 0.59765625

Factor a perfect square on the left side:
(t2 + 0.3125)(t2 + 0.3125) = 0.59765625

Calculate the square root of the right side: 0.773082305

Break this problem into two subproblems by setting 
(t2 + 0.3125) equal to 0.773082305 and -0.773082305.

Subproblem 1

t2 + 0.3125 = 0.773082305 Simplifying t2 + 0.3125 = 0.773082305 Reorder the terms: 0.3125 + t2 = 0.773082305 Solving 0.3125 + t2 = 0.773082305 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t2 = 0.773082305 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t2 = 0.773082305 + -0.3125 t2 = 0.773082305 + -0.3125 Combine like terms: 0.773082305 + -0.3125 = 0.460582305 t2 = 0.460582305 Simplifying t2 = 0.460582305 Take the square root of each side: t = {-0.678662143, 0.678662143}

Subproblem 2

t2 + 0.3125 = -0.773082305 Simplifying t2 + 0.3125 = -0.773082305 Reorder the terms: 0.3125 + t2 = -0.773082305 Solving 0.3125 + t2 = -0.773082305 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t2 = -0.773082305 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t2 = -0.773082305 + -0.3125 t2 = -0.773082305 + -0.3125 Combine like terms: -0.773082305 + -0.3125 = -1.085582305 t2 = -1.085582305 Simplifying t2 = -1.085582305 Reorder the terms: 1.085582305 + t2 = -1.085582305 + 1.085582305 Combine like terms: -1.085582305 + 1.085582305 = 0.000000000 1.085582305 + 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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