t^2-248t+676=0

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Solution for t^2-248t+676=0 equation: 


Simplifying
t2 + -248t + 676 = 0

Reorder the terms:
676 + -248t + t2 = 0

Solving
676 + -248t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-676' to each side of the equation.
676 + -248t + -676 + t2 = 0 + -676

Reorder the terms:
676 + -676 + -248t + t2 = 0 + -676

Combine like terms: 676 + -676 = 0
0 + -248t + t2 = 0 + -676
-248t + t2 = 0 + -676

Combine like terms: 0 + -676 = -676
-248t + t2 = -676

The t term is -248t.  Take half its coefficient (-124).
Square it (15376) and add it to both sides.

Add '15376' to each side of the equation.
-248t + 15376 + t2 = -676 + 15376

Reorder the terms:
15376 + -248t + t2 = -676 + 15376

Combine like terms: -676 + 15376 = 14700
15376 + -248t + t2 = 14700

Factor a perfect square on the left side:
(t + -124)(t + -124) = 14700

Calculate the square root of the right side: 121.24355653

Break this problem into two subproblems by setting 
(t + -124) equal to 121.24355653 and -121.24355653.


Subproblem 1
t + -124 = 121.24355653

Simplifying
t + -124 = 121.24355653

Reorder the terms:
-124 + t = 121.24355653

Solving
-124 + t = 121.24355653

Solving for variable 't'.

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

Add '124' to each side of the equation.
-124 + 124 + t = 121.24355653 + 124

Combine like terms: -124 + 124 = 0
0 + t = 121.24355653 + 124
t = 121.24355653 + 124

Combine like terms: 121.24355653 + 124 = 245.24355653
t = 245.24355653

Simplifying
t = 245.24355653


Subproblem 2
t + -124 = -121.24355653

Simplifying
t + -124 = -121.24355653

Reorder the terms:
-124 + t = -121.24355653

Solving
-124 + t = -121.24355653

Solving for variable 't'.

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

Add '124' to each side of the equation.
-124 + 124 + t = -121.24355653 + 124

Combine like terms: -124 + 124 = 0
0 + t = -121.24355653 + 124
t = -121.24355653 + 124

Combine like terms: -121.24355653 + 124 = 2.75644347
t = 2.75644347

Simplifying
t = 2.75644347


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {245.24355653, 2.75644347}

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