5t^2+10t+25=180

Solution for 5t^2+10t+25=180 equation:

Simplifying
5t2 + 10t + 25 = 180

Reorder the terms:
25 + 10t + 5t2 = 180

Solving
25 + 10t + 5t2 = 180

Solving for variable 't'.

Reorder the terms:
25 + -180 + 10t + 5t2 = 180 + -180

Combine like terms: 25 + -180 = -155
-155 + 10t + 5t2 = 180 + -180

Combine like terms: 180 + -180 = 0
-155 + 10t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-31 + 2t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-31 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
-31 + 2t + t2 = 0

Solving
-31 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 2t + 31 + t2 = 0 + 31

Reorder the terms:
-31 + 31 + 2t + t2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2t + t2 = 0 + 31
2t + t2 = 0 + 31

Combine like terms: 0 + 31 = 31
2t + t2 = 31

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 31 + 1

Reorder the terms:
1 + 2t + t2 = 31 + 1

Combine like terms: 31 + 1 = 32
1 + 2t + t2 = 32

Factor a perfect square on the left side:
(t + 1)(t + 1) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(t + 1) equal to 5.656854249 and -5.656854249.

Subproblem 1
t + 1 = 5.656854249

Simplifying
t + 1 = 5.656854249

Reorder the terms:
1 + t = 5.656854249

Solving
1 + t = 5.656854249

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 5.656854249 + -1

Combine like terms: 1 + -1 = 0
0 + t = 5.656854249 + -1
t = 5.656854249 + -1

Combine like terms: 5.656854249 + -1 = 4.656854249
t = 4.656854249

Simplifying
t = 4.656854249

Subproblem 2
t + 1 = -5.656854249

Simplifying
t + 1 = -5.656854249

Reorder the terms:
1 + t = -5.656854249

Solving
1 + t = -5.656854249

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -5.656854249 + -1

Combine like terms: 1 + -1 = 0
0 + t = -5.656854249 + -1
t = -5.656854249 + -1

Combine like terms: -5.656854249 + -1 = -6.656854249
t = -6.656854249

Simplifying
t = -6.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.656854249, -6.656854249}
Solution
t = {4.656854249, -6.656854249}