2t^2+40t+34=0

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Solution for 2t^2+40t+34=0 equation: 


Simplifying
2t2 + 40t + 34 = 0

Reorder the terms:
34 + 40t + 2t2 = 0

Solving
34 + 40t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 20t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + 20t + t2)' equal to zero and attempt to solve:

Simplifying
17 + 20t + t2 = 0

Solving
17 + 20t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 20t + -17 + t2 = 0 + -17

Reorder the terms:
17 + -17 + 20t + t2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 20t + t2 = 0 + -17
20t + t2 = 0 + -17

Combine like terms: 0 + -17 = -17
20t + t2 = -17

The t term is 20t.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20t + 100 + t2 = -17 + 100

Reorder the terms:
100 + 20t + t2 = -17 + 100

Combine like terms: -17 + 100 = 83
100 + 20t + t2 = 83

Factor a perfect square on the left side:
(t + 10)(t + 10) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(t + 10) equal to 9.110433579 and -9.110433579.


Subproblem 1
t + 10 = 9.110433579

Simplifying
t + 10 = 9.110433579

Reorder the terms:
10 + t = 9.110433579

Solving
10 + t = 9.110433579

Solving for variable 't'.

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

Add '-10' to each side of the equation.
10 + -10 + t = 9.110433579 + -10

Combine like terms: 10 + -10 = 0
0 + t = 9.110433579 + -10
t = 9.110433579 + -10

Combine like terms: 9.110433579 + -10 = -0.889566421
t = -0.889566421

Simplifying
t = -0.889566421


Subproblem 2
t + 10 = -9.110433579

Simplifying
t + 10 = -9.110433579

Reorder the terms:
10 + t = -9.110433579

Solving
10 + t = -9.110433579

Solving for variable 't'.

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

Add '-10' to each side of the equation.
10 + -10 + t = -9.110433579 + -10

Combine like terms: 10 + -10 = 0
0 + t = -9.110433579 + -10
t = -9.110433579 + -10

Combine like terms: -9.110433579 + -10 = -19.110433579
t = -19.110433579

Simplifying
t = -19.110433579


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.889566421, -19.110433579}
Solution
t = {-0.889566421, -19.110433579}

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