t^2+6.1t+2.4=0

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Solution for t^2+6.1t+2.4=0 equation: 


Simplifying
t2 + 6.1t + 2.4 = 0

Reorder the terms:
2.4 + 6.1t + t2 = 0

Solving
2.4 + 6.1t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 6.1t + -2.4 + t2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 6.1t + t2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 6.1t + t2 = 0 + -2.4
6.1t + t2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
6.1t + t2 = -2.4

The t term is 6.1t.  Take half its coefficient (3.05).
Square it (9.3025) and add it to both sides.

Add '9.3025' to each side of the equation.
6.1t + 9.3025 + t2 = -2.4 + 9.3025

Reorder the terms:
9.3025 + 6.1t + t2 = -2.4 + 9.3025

Combine like terms: -2.4 + 9.3025 = 6.9025
9.3025 + 6.1t + t2 = 6.9025

Factor a perfect square on the left side:
(t + 3.05)(t + 3.05) = 6.9025

Calculate the square root of the right side: 2.627260931

Break this problem into two subproblems by setting 
(t + 3.05) equal to 2.627260931 and -2.627260931.


Subproblem 1
t + 3.05 = 2.627260931

Simplifying
t + 3.05 = 2.627260931

Reorder the terms:
3.05 + t = 2.627260931

Solving
3.05 + t = 2.627260931

Solving for variable 't'.

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

Add '-3.05' to each side of the equation.
3.05 + -3.05 + t = 2.627260931 + -3.05

Combine like terms: 3.05 + -3.05 = 0.00
0.00 + t = 2.627260931 + -3.05
t = 2.627260931 + -3.05

Combine like terms: 2.627260931 + -3.05 = -0.422739069
t = -0.422739069

Simplifying
t = -0.422739069


Subproblem 2
t + 3.05 = -2.627260931

Simplifying
t + 3.05 = -2.627260931

Reorder the terms:
3.05 + t = -2.627260931

Solving
3.05 + t = -2.627260931

Solving for variable 't'.

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

Add '-3.05' to each side of the equation.
3.05 + -3.05 + t = -2.627260931 + -3.05

Combine like terms: 3.05 + -3.05 = 0.00
0.00 + t = -2.627260931 + -3.05
t = -2.627260931 + -3.05

Combine like terms: -2.627260931 + -3.05 = -5.677260931
t = -5.677260931

Simplifying
t = -5.677260931


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.422739069, -5.677260931}

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