3.75t^2+2.7t-2=0

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Solution for 3.75t^2+2.7t-2=0 equation: 


Simplifying
3.75t2 + 2.7t + -2 = 0

Reorder the terms:
-2 + 2.7t + 3.75t2 = 0

Solving
-2 + 2.7t + 3.75t2 = 0

Solving for variable 't'.

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

Divide each side by '3.75'.
-0.5333333333 + 0.72t + t2 = 0

Move the constant term to the right:

Add '0.5333333333' to each side of the equation.
-0.5333333333 + 0.72t + 0.5333333333 + t2 = 0 + 0.5333333333

Reorder the terms:
-0.5333333333 + 0.5333333333 + 0.72t + t2 = 0 + 0.5333333333

Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000
0.0000000000 + 0.72t + t2 = 0 + 0.5333333333
0.72t + t2 = 0 + 0.5333333333

Combine like terms: 0 + 0.5333333333 = 0.5333333333
0.72t + t2 = 0.5333333333

The t term is 0.72t.  Take half its coefficient (0.36).
Square it (0.1296) and add it to both sides.

Add '0.1296' to each side of the equation.
0.72t + 0.1296 + t2 = 0.5333333333 + 0.1296

Reorder the terms:
0.1296 + 0.72t + t2 = 0.5333333333 + 0.1296

Combine like terms: 0.5333333333 + 0.1296 = 0.6629333333
0.1296 + 0.72t + t2 = 0.6629333333

Factor a perfect square on the left side:
(t + 0.36)(t + 0.36) = 0.6629333333

Calculate the square root of the right side: 0.814207181

Break this problem into two subproblems by setting 
(t + 0.36) equal to 0.814207181 and -0.814207181.


Subproblem 1
t + 0.36 = 0.814207181

Simplifying
t + 0.36 = 0.814207181

Reorder the terms:
0.36 + t = 0.814207181

Solving
0.36 + t = 0.814207181

Solving for variable 't'.

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

Add '-0.36' to each side of the equation.
0.36 + -0.36 + t = 0.814207181 + -0.36

Combine like terms: 0.36 + -0.36 = 0.00
0.00 + t = 0.814207181 + -0.36
t = 0.814207181 + -0.36

Combine like terms: 0.814207181 + -0.36 = 0.454207181
t = 0.454207181

Simplifying
t = 0.454207181


Subproblem 2
t + 0.36 = -0.814207181

Simplifying
t + 0.36 = -0.814207181

Reorder the terms:
0.36 + t = -0.814207181

Solving
0.36 + t = -0.814207181

Solving for variable 't'.

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

Add '-0.36' to each side of the equation.
0.36 + -0.36 + t = -0.814207181 + -0.36

Combine like terms: 0.36 + -0.36 = 0.00
0.00 + t = -0.814207181 + -0.36
t = -0.814207181 + -0.36

Combine like terms: -0.814207181 + -0.36 = -1.174207181
t = -1.174207181

Simplifying
t = -1.174207181


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.454207181, -1.174207181}

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