10t^2+11t+2=

Solution for 10t^2+11t+2= equation:

Simplifying
10t2 + 11t + 2 = 0

Reorder the terms:
2 + 11t + 10t2 = 0

Solving
2 + 11t + 10t2 = 0

Solving for variable 't'.

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

Divide each side by '10'.
0.2 + 1.1t + t2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.1t + -0.2 + t2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.1t + t2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.1t + t2 = 0 + -0.2
1.1t + t2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.1t + t2 = -0.2

The t term is 1.1t.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1t + 0.3025 + t2 = -0.2 + 0.3025

Reorder the terms:
0.3025 + 1.1t + t2 = -0.2 + 0.3025

Combine like terms: -0.2 + 0.3025 = 0.1025
0.3025 + 1.1t + t2 = 0.1025

Factor a perfect square on the left side:
(t + 0.55)(t + 0.55) = 0.1025

Calculate the square root of the right side: 0.320156212

Break this problem into two subproblems by setting 
(t + 0.55) equal to 0.320156212 and -0.320156212.

Subproblem 1
t + 0.55 = 0.320156212

Simplifying
t + 0.55 = 0.320156212

Reorder the terms:
0.55 + t = 0.320156212

Solving
0.55 + t = 0.320156212

Solving for variable 't'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + t = 0.320156212 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + t = 0.320156212 + -0.55
t = 0.320156212 + -0.55

Combine like terms: 0.320156212 + -0.55 = -0.229843788
t = -0.229843788

Simplifying
t = -0.229843788

Subproblem 2
t + 0.55 = -0.320156212

Simplifying
t + 0.55 = -0.320156212

Reorder the terms:
0.55 + t = -0.320156212

Solving
0.55 + t = -0.320156212

Solving for variable 't'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + t = -0.320156212 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + t = -0.320156212 + -0.55
t = -0.320156212 + -0.55

Combine like terms: -0.320156212 + -0.55 = -0.870156212
t = -0.870156212

Simplifying
t = -0.870156212

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.229843788, -0.870156212}