t^2-15t-50=0

Solution for t^2-15t-50=0 equation:

Simplifying
t2 + -15t + -50 = 0

Reorder the terms:
-50 + -15t + t2 = 0

Solving
-50 + -15t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -15t + 50 + t2 = 0 + 50

Reorder the terms:
-50 + 50 + -15t + t2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -15t + t2 = 0 + 50
-15t + t2 = 0 + 50

Combine like terms: 0 + 50 = 50
-15t + t2 = 50

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 = 50 + 56.25

Reorder the terms:
56.25 + -15t + t2 = 50 + 56.25

Combine like terms: 50 + 56.25 = 106.25
56.25 + -15t + t2 = 106.25

Factor a perfect square on the left side:
(t + -7.5)(t + -7.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(t + -7.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
t + -7.5 = 10.307764064

Simplifying
t + -7.5 = 10.307764064

Reorder the terms:
-7.5 + t = 10.307764064

Solving
-7.5 + t = 10.307764064

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 = 10.307764064 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + t = 10.307764064 + 7.5
t = 10.307764064 + 7.5

Combine like terms: 10.307764064 + 7.5 = 17.807764064
t = 17.807764064

Simplifying
t = 17.807764064

Subproblem 2
t + -7.5 = -10.307764064

Simplifying
t + -7.5 = -10.307764064

Reorder the terms:
-7.5 + t = -10.307764064

Solving
-7.5 + t = -10.307764064

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 = -10.307764064 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + t = -10.307764064 + 7.5
t = -10.307764064 + 7.5

Combine like terms: -10.307764064 + 7.5 = -2.807764064
t = -2.807764064

Simplifying
t = -2.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {17.807764064, -2.807764064}