Simplifying
10t^{2} = t + 2
Reorder the terms:
10t^{2} = 2 + t
Solving
10t^{2} = 2 + t
Solving for variable 't'.
Reorder the terms:
-2 + -1t + 10t^{2} = 2 + t + -2 + -1t
Reorder the terms:
-2 + -1t + 10t^{2} = 2 + -2 + t + -1t
Combine like terms: 2 + -2 = 0
-2 + -1t + 10t^{2} = 0 + t + -1t
-2 + -1t + 10t^{2} = t + -1t
Combine like terms: t + -1t = 0
-2 + -1t + 10t^{2} = 0
Begin completing the square. Divide all terms by
10 the coefficient of the squared term:
Divide each side by '10'.
-0.2 + -0.1t + t^{2} = 0
Move the constant term to the right:
Add '0.2' to each side of the equation.
-0.2 + -0.1t + 0.2 + t^{2} = 0 + 0.2
Reorder the terms:
-0.2 + 0.2 + -0.1t + t^{2} = 0 + 0.2
Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.1t + t^{2} = 0 + 0.2
-0.1t + t^{2} = 0 + 0.2
Combine like terms: 0 + 0.2 = 0.2
-0.1t + t^{2} = 0.2
The t term is -0.1t. Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.
Add '0.0025' to each side of the equation.
-0.1t + 0.0025 + t^{2} = 0.2 + 0.0025
Reorder the terms:
0.0025 + -0.1t + t^{2} = 0.2 + 0.0025
Combine like terms: 0.2 + 0.0025 = 0.2025
0.0025 + -0.1t + t^{2} = 0.2025
Factor a perfect square on the left side:
(t + -0.05)(t + -0.05) = 0.2025
Calculate the square root of the right side: 0.45
Break this problem into two subproblems by setting
(t + -0.05) equal to 0.45 and -0.45.
#### Subproblem 1

t + -0.05 = 0.45
Simplifying
t + -0.05 = 0.45
Reorder the terms:
-0.05 + t = 0.45
Solving
-0.05 + t = 0.45
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '0.05' to each side of the equation.
-0.05 + 0.05 + t = 0.45 + 0.05
Combine like terms: -0.05 + 0.05 = 0.00
0.00 + t = 0.45 + 0.05
t = 0.45 + 0.05
Combine like terms: 0.45 + 0.05 = 0.5
t = 0.5
Simplifying
t = 0.5
#### Subproblem 2

t + -0.05 = -0.45
Simplifying
t + -0.05 = -0.45
Reorder the terms:
-0.05 + t = -0.45
Solving
-0.05 + t = -0.45
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '0.05' to each side of the equation.
-0.05 + 0.05 + t = -0.45 + 0.05
Combine like terms: -0.05 + 0.05 = 0.00
0.00 + t = -0.45 + 0.05
t = -0.45 + 0.05
Combine like terms: -0.45 + 0.05 = -0.4
t = -0.4
Simplifying
t = -0.4
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
t = {0.5, -0.4}