t^2+15t+56.25=45.25

Solution for t^2+15t+56.25=45.25 equation:

Simplifying
t2 + 15t + 56.25 = 45.25

Reorder the terms:
56.25 + 15t + t2 = 45.25

Solving
56.25 + 15t + t2 = 45.25

Solving for variable 't'.

Reorder the terms:
56.25 + -45.25 + 15t + t2 = 45.25 + -45.25

Combine like terms: 56.25 + -45.25 = 11
11 + 15t + t2 = 45.25 + -45.25

Combine like terms: 45.25 + -45.25 = 0.00
11 + 15t + t2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 15t + -11 + t2 = 0.00 + -11

Reorder the terms:
11 + -11 + 15t + t2 = 0.00 + -11

Combine like terms: 11 + -11 = 0
0 + 15t + t2 = 0.00 + -11
15t + t2 = 0.00 + -11

Combine like terms: 0.00 + -11 = -11
15t + t2 = -11

The t term is 15t.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15t + 56.25 + t2 = -11 + 56.25

Reorder the terms:
56.25 + 15t + t2 = -11 + 56.25

Combine like terms: -11 + 56.25 = 45.25
56.25 + 15t + t2 = 45.25

Factor a perfect square on the left side:
(t + 7.5)(t + 7.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(t + 7.5) equal to 6.726812024 and -6.726812024.

Subproblem 1
t + 7.5 = 6.726812024

Simplifying
t + 7.5 = 6.726812024

Reorder the terms:
7.5 + t = 6.726812024

Solving
7.5 + t = 6.726812024

Solving for variable 't'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + t = 6.726812024 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + t = 6.726812024 + -7.5
t = 6.726812024 + -7.5

Combine like terms: 6.726812024 + -7.5 = -0.773187976
t = -0.773187976

Simplifying
t = -0.773187976

Subproblem 2
t + 7.5 = -6.726812024

Simplifying
t + 7.5 = -6.726812024

Reorder the terms:
7.5 + t = -6.726812024

Solving
7.5 + t = -6.726812024

Solving for variable 't'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + t = -6.726812024 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + t = -6.726812024 + -7.5
t = -6.726812024 + -7.5

Combine like terms: -6.726812024 + -7.5 = -14.226812024
t = -14.226812024

Simplifying
t = -14.226812024

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.773187976, -14.226812024}