(t^2)-25t-12.5=0

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Solution for (t^2)-25t-12.5=0 equation: 


Simplifying
(t2) + -25t + -12.5 = 0
t2 + -25t + -12.5 = 0

Reorder the terms:
-12.5 + -25t + t2 = 0

Solving
-12.5 + -25t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -25t + 12.5 + t2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -25t + t2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -25t + t2 = 0 + 12.5
-25t + t2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-25t + t2 = 12.5

The t term is -25t.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25t + 156.25 + t2 = 12.5 + 156.25

Reorder the terms:
156.25 + -25t + t2 = 12.5 + 156.25

Combine like terms: 12.5 + 156.25 = 168.75
156.25 + -25t + t2 = 168.75

Factor a perfect square on the left side:
(t + -12.5)(t + -12.5) = 168.75

Calculate the square root of the right side: 12.990381057

Break this problem into two subproblems by setting 
(t + -12.5) equal to 12.990381057 and -12.990381057.


Subproblem 1
t + -12.5 = 12.990381057

Simplifying
t + -12.5 = 12.990381057

Reorder the terms:
-12.5 + t = 12.990381057

Solving
-12.5 + t = 12.990381057

Solving for variable 't'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + t = 12.990381057 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + t = 12.990381057 + 12.5
t = 12.990381057 + 12.5

Combine like terms: 12.990381057 + 12.5 = 25.490381057
t = 25.490381057

Simplifying
t = 25.490381057


Subproblem 2
t + -12.5 = -12.990381057

Simplifying
t + -12.5 = -12.990381057

Reorder the terms:
-12.5 + t = -12.990381057

Solving
-12.5 + t = -12.990381057

Solving for variable 't'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + t = -12.990381057 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + t = -12.990381057 + 12.5
t = -12.990381057 + 12.5

Combine like terms: -12.990381057 + 12.5 = -0.490381057
t = -0.490381057

Simplifying
t = -0.490381057


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {25.490381057, -0.490381057}

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