0.7t^2-3.5t-1.75=0

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Solution for 0.7t^2-3.5t-1.75=0 equation: 


Simplifying
0.7t2 + -3.5t + -1.75 = 0

Reorder the terms:
-1.75 + -3.5t + 0.7t2 = 0

Solving
-1.75 + -3.5t + 0.7t2 = 0

Solving for variable 't'.

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

Divide each side by '0.7'.
-2.5 + -5t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -5t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -5t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -5t + t2 = 0 + 2.5
-5t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-5t + t2 = 2.5

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 = 2.5 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 2.5 + 6.25

Combine like terms: 2.5 + 6.25 = 8.75
6.25 + -5t + t2 = 8.75

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.958039892 and -2.958039892.


Subproblem 1
t + -2.5 = 2.958039892

Simplifying
t + -2.5 = 2.958039892

Reorder the terms:
-2.5 + t = 2.958039892

Solving
-2.5 + t = 2.958039892

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 = 2.958039892 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.958039892 + 2.5
t = 2.958039892 + 2.5

Combine like terms: 2.958039892 + 2.5 = 5.458039892
t = 5.458039892

Simplifying
t = 5.458039892


Subproblem 2
t + -2.5 = -2.958039892

Simplifying
t + -2.5 = -2.958039892

Reorder the terms:
-2.5 + t = -2.958039892

Solving
-2.5 + t = -2.958039892

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 = -2.958039892 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.958039892 + 2.5
t = -2.958039892 + 2.5

Combine like terms: -2.958039892 + 2.5 = -0.458039892
t = -0.458039892

Simplifying
t = -0.458039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.458039892, -0.458039892}

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