t^2-24t-125=0

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Solution for t^2-24t-125=0 equation: 


Simplifying
t2 + -24t + -125 = 0

Reorder the terms:
-125 + -24t + t2 = 0

Solving
-125 + -24t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -24t + 125 + t2 = 0 + 125

Reorder the terms:
-125 + 125 + -24t + t2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -24t + t2 = 0 + 125
-24t + t2 = 0 + 125

Combine like terms: 0 + 125 = 125
-24t + t2 = 125

The t term is -24t.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24t + 144 + t2 = 125 + 144

Reorder the terms:
144 + -24t + t2 = 125 + 144

Combine like terms: 125 + 144 = 269
144 + -24t + t2 = 269

Factor a perfect square on the left side:
(t + -12)(t + -12) = 269

Calculate the square root of the right side: 16.401219467

Break this problem into two subproblems by setting 
(t + -12) equal to 16.401219467 and -16.401219467.


Subproblem 1
t + -12 = 16.401219467

Simplifying
t + -12 = 16.401219467

Reorder the terms:
-12 + t = 16.401219467

Solving
-12 + t = 16.401219467

Solving for variable 't'.

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

Add '12' to each side of the equation.
-12 + 12 + t = 16.401219467 + 12

Combine like terms: -12 + 12 = 0
0 + t = 16.401219467 + 12
t = 16.401219467 + 12

Combine like terms: 16.401219467 + 12 = 28.401219467
t = 28.401219467

Simplifying
t = 28.401219467


Subproblem 2
t + -12 = -16.401219467

Simplifying
t + -12 = -16.401219467

Reorder the terms:
-12 + t = -16.401219467

Solving
-12 + t = -16.401219467

Solving for variable 't'.

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

Add '12' to each side of the equation.
-12 + 12 + t = -16.401219467 + 12

Combine like terms: -12 + 12 = 0
0 + t = -16.401219467 + 12
t = -16.401219467 + 12

Combine like terms: -16.401219467 + 12 = -4.401219467
t = -4.401219467

Simplifying
t = -4.401219467


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {28.401219467, -4.401219467}

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