t+2t^2=43

Solution for t+2t^2=43 equation:

Simplifying
t + 2t2 = 43

Solving
t + 2t2 = 43

Solving for variable 't'.

Reorder the terms:
-43 + t + 2t2 = 43 + -43

Combine like terms: 43 + -43 = 0
-43 + t + 2t2 = 0

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

Divide each side by '2'.
-21.5 + 0.5t + t2 = 0

Move the constant term to the right:

Add '21.5' to each side of the equation.
-21.5 + 0.5t + 21.5 + t2 = 0 + 21.5

Reorder the terms:
-21.5 + 21.5 + 0.5t + t2 = 0 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + 0.5t + t2 = 0 + 21.5
0.5t + t2 = 0 + 21.5

Combine like terms: 0 + 21.5 = 21.5
0.5t + t2 = 21.5

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5t + 0.25 + t2 = 21.5 + 0.25

Reorder the terms:
0.25 + 0.5t + t2 = 21.5 + 0.25

Combine like terms: 21.5 + 0.25 = 21.75
0.25 + 0.5t + t2 = 21.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 21.75

Calculate the square root of the right side: 4.663689527

Break this problem into two subproblems by setting 
(t + 0.5) equal to 4.663689527 and -4.663689527.

Subproblem 1
t + 0.5 = 4.663689527

Simplifying
t + 0.5 = 4.663689527

Reorder the terms:
0.5 + t = 4.663689527

Solving
0.5 + t = 4.663689527

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 4.663689527 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 4.663689527 + -0.5
t = 4.663689527 + -0.5

Combine like terms: 4.663689527 + -0.5 = 4.163689527
t = 4.163689527

Simplifying
t = 4.163689527

Subproblem 2
t + 0.5 = -4.663689527

Simplifying
t + 0.5 = -4.663689527

Reorder the terms:
0.5 + t = -4.663689527

Solving
0.5 + t = -4.663689527

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -4.663689527 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -4.663689527 + -0.5
t = -4.663689527 + -0.5

Combine like terms: -4.663689527 + -0.5 = -5.163689527
t = -5.163689527

Simplifying
t = -5.163689527

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.163689527, -5.163689527}