0=t^2-50t+35

Solution for 0=t^2-50t+35 equation:

Simplifying
0 = t2 + -50t + 35

Reorder the terms:
0 = 35 + -50t + t2

Solving
0 = 35 + -50t + t2

Solving for variable 't'.

Combine like terms: 0 + -35 = -35
-35 + 50t + -1t2 = 35 + -50t + t2 + -35 + 50t + -1t2

Reorder the terms:
-35 + 50t + -1t2 = 35 + -35 + -50t + 50t + t2 + -1t2

Combine like terms: 35 + -35 = 0
-35 + 50t + -1t2 = 0 + -50t + 50t + t2 + -1t2
-35 + 50t + -1t2 = -50t + 50t + t2 + -1t2

Combine like terms: -50t + 50t = 0
-35 + 50t + -1t2 = 0 + t2 + -1t2
-35 + 50t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-35 + 50t + -1t2 = 0

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

Divide each side by '-1'.
35 + -50t + t2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -50t + -35 + t2 = 0 + -35

Reorder the terms:
35 + -35 + -50t + t2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -50t + t2 = 0 + -35
-50t + t2 = 0 + -35

Combine like terms: 0 + -35 = -35
-50t + t2 = -35

The t term is -50t.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50t + 625 + t2 = -35 + 625

Reorder the terms:
625 + -50t + t2 = -35 + 625

Combine like terms: -35 + 625 = 590
625 + -50t + t2 = 590

Factor a perfect square on the left side:
(t + -25)(t + -25) = 590

Calculate the square root of the right side: 24.289915603

Break this problem into two subproblems by setting 
(t + -25) equal to 24.289915603 and -24.289915603.

Subproblem 1
t + -25 = 24.289915603

Simplifying
t + -25 = 24.289915603

Reorder the terms:
-25 + t = 24.289915603

Solving
-25 + t = 24.289915603

Solving for variable 't'.

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

Add '25' to each side of the equation.
-25 + 25 + t = 24.289915603 + 25

Combine like terms: -25 + 25 = 0
0 + t = 24.289915603 + 25
t = 24.289915603 + 25

Combine like terms: 24.289915603 + 25 = 49.289915603
t = 49.289915603

Simplifying
t = 49.289915603

Subproblem 2
t + -25 = -24.289915603

Simplifying
t + -25 = -24.289915603

Reorder the terms:
-25 + t = -24.289915603

Solving
-25 + t = -24.289915603

Solving for variable 't'.

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

Add '25' to each side of the equation.
-25 + 25 + t = -24.289915603 + 25

Combine like terms: -25 + 25 = 0
0 + t = -24.289915603 + 25
t = -24.289915603 + 25

Combine like terms: -24.289915603 + 25 = 0.710084397
t = 0.710084397

Simplifying
t = 0.710084397

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {49.289915603, 0.710084397}