t^2-15t+56.25=0

Solution for t^2-15t+56.25=0 equation:

Simplifying
t2 + -15t + 56.25 = 0

Reorder the terms:
56.25 + -15t + t2 = 0

Solving
56.25 + -15t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-56.25' to each side of the equation.
56.25 + -15t + -56.25 + t2 = 0 + -56.25

Reorder the terms:
56.25 + -56.25 + -15t + t2 = 0 + -56.25

Combine like terms: 56.25 + -56.25 = 0.00
0.00 + -15t + t2 = 0 + -56.25
-15t + t2 = 0 + -56.25

Combine like terms: 0 + -56.25 = -56.25
-15t + t2 = -56.25

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 = -56.25 + 56.25

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

Combine like terms: -56.25 + 56.25 = 0.00
56.25 + -15t + t2 = 0.00

Factor a perfect square on the left side:
(t + -7.5)(t + -7.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(t + -7.5) equal to 0.00 and 0.00.

Subproblem 1
t + -7.5 = 0.00

Simplifying
t + -7.5 = 0.00

Reorder the terms:
-7.5 + t = 0.00

Solving
-7.5 + t = 0.00

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 = 0.00 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + t = 0.00 + 7.5
t = 0.00 + 7.5

Combine like terms: 0.00 + 7.5 = 7.5
t = 7.5

Simplifying
t = 7.5

Subproblem 2
t + -7.5 = 0.00

Simplifying
t + -7.5 = 0.00

Reorder the terms:
-7.5 + t = 0.00

Solving
-7.5 + t = 0.00

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 = 0.00 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + t = 0.00 + 7.5
t = 0.00 + 7.5

Combine like terms: 0.00 + 7.5 = 7.5
t = 7.5

Simplifying
t = 7.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.5, 7.5}