38=5t^2+20t+18

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Solution for 38=5t^2+20t+18 equation: 


Simplifying
38 = 5t2 + 20t + 18

Reorder the terms:
38 = 18 + 20t + 5t2

Solving
38 = 18 + 20t + 5t2

Solving for variable 't'.

Combine like terms: 38 + -18 = 20
20 + -20t + -5t2 = 18 + 20t + 5t2 + -18 + -20t + -5t2

Reorder the terms:
20 + -20t + -5t2 = 18 + -18 + 20t + -20t + 5t2 + -5t2

Combine like terms: 18 + -18 = 0
20 + -20t + -5t2 = 0 + 20t + -20t + 5t2 + -5t2
20 + -20t + -5t2 = 20t + -20t + 5t2 + -5t2

Combine like terms: 20t + -20t = 0
20 + -20t + -5t2 = 0 + 5t2 + -5t2
20 + -20t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
20 + -20t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -4t + -1t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + -4t + -1t2)' equal to zero and attempt to solve:

Simplifying
4 + -4t + -1t2 = 0

Solving
4 + -4t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 4t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 4t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4t + t2 = 0 + 4
4t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
4t + t2 = 4

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 4 + 4

Reorder the terms:
4 + 4t + t2 = 4 + 4

Combine like terms: 4 + 4 = 8
4 + 4t + t2 = 8

Factor a perfect square on the left side:
(t + 2)(t + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(t + 2) equal to 2.828427125 and -2.828427125.


Subproblem 1
t + 2 = 2.828427125

Simplifying
t + 2 = 2.828427125

Reorder the terms:
2 + t = 2.828427125

Solving
2 + t = 2.828427125

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + t = 2.828427125 + -2
t = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
t = 0.828427125

Simplifying
t = 0.828427125


Subproblem 2
t + 2 = -2.828427125

Simplifying
t + 2 = -2.828427125

Reorder the terms:
2 + t = -2.828427125

Solving
2 + t = -2.828427125

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + t = -2.828427125 + -2
t = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
t = -4.828427125

Simplifying
t = -4.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.828427125, -4.828427125}
Solution
t = {0.828427125, -4.828427125}

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