5t^2+25t+2=0

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Solution for 5t^2+25t+2=0 equation: 


Simplifying
5t2 + 25t + 2 = 0

Reorder the terms:
2 + 25t + 5t2 = 0

Solving
2 + 25t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
0.4 + 5t + t2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 5t + -0.4 + t2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 5t + t2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 5t + t2 = 0 + -0.4
5t + t2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
5t + t2 = -0.4

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = -0.4 + 6.25

Reorder the terms:
6.25 + 5t + t2 = -0.4 + 6.25

Combine like terms: -0.4 + 6.25 = 5.85
6.25 + 5t + t2 = 5.85

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 5.85

Calculate the square root of the right side: 2.418677324

Break this problem into two subproblems by setting 
(t + 2.5) equal to 2.418677324 and -2.418677324.


Subproblem 1
t + 2.5 = 2.418677324

Simplifying
t + 2.5 = 2.418677324

Reorder the terms:
2.5 + t = 2.418677324

Solving
2.5 + t = 2.418677324

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 2.418677324 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 2.418677324 + -2.5
t = 2.418677324 + -2.5

Combine like terms: 2.418677324 + -2.5 = -0.081322676
t = -0.081322676

Simplifying
t = -0.081322676


Subproblem 2
t + 2.5 = -2.418677324

Simplifying
t + 2.5 = -2.418677324

Reorder the terms:
2.5 + t = -2.418677324

Solving
2.5 + t = -2.418677324

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -2.418677324 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -2.418677324 + -2.5
t = -2.418677324 + -2.5

Combine like terms: -2.418677324 + -2.5 = -4.918677324
t = -4.918677324

Simplifying
t = -4.918677324


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.081322676, -4.918677324}

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