t^2-18.5t-174.5=0

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Solution for t^2-18.5t-174.5=0 equation: 


Simplifying
t2 + -18.5t + -174.5 = 0

Reorder the terms:
-174.5 + -18.5t + t2 = 0

Solving
-174.5 + -18.5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '174.5' to each side of the equation.
-174.5 + -18.5t + 174.5 + t2 = 0 + 174.5

Reorder the terms:
-174.5 + 174.5 + -18.5t + t2 = 0 + 174.5

Combine like terms: -174.5 + 174.5 = 0.0
0.0 + -18.5t + t2 = 0 + 174.5
-18.5t + t2 = 0 + 174.5

Combine like terms: 0 + 174.5 = 174.5
-18.5t + t2 = 174.5

The t term is -18.5t.  Take half its coefficient (-9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
-18.5t + 85.5625 + t2 = 174.5 + 85.5625

Reorder the terms:
85.5625 + -18.5t + t2 = 174.5 + 85.5625

Combine like terms: 174.5 + 85.5625 = 260.0625
85.5625 + -18.5t + t2 = 260.0625

Factor a perfect square on the left side:
(t + -9.25)(t + -9.25) = 260.0625

Calculate the square root of the right side: 16.126453423

Break this problem into two subproblems by setting 
(t + -9.25) equal to 16.126453423 and -16.126453423.


Subproblem 1
t + -9.25 = 16.126453423

Simplifying
t + -9.25 = 16.126453423

Reorder the terms:
-9.25 + t = 16.126453423

Solving
-9.25 + t = 16.126453423

Solving for variable 't'.

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

Add '9.25' to each side of the equation.
-9.25 + 9.25 + t = 16.126453423 + 9.25

Combine like terms: -9.25 + 9.25 = 0.00
0.00 + t = 16.126453423 + 9.25
t = 16.126453423 + 9.25

Combine like terms: 16.126453423 + 9.25 = 25.376453423
t = 25.376453423

Simplifying
t = 25.376453423


Subproblem 2
t + -9.25 = -16.126453423

Simplifying
t + -9.25 = -16.126453423

Reorder the terms:
-9.25 + t = -16.126453423

Solving
-9.25 + t = -16.126453423

Solving for variable 't'.

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

Add '9.25' to each side of the equation.
-9.25 + 9.25 + t = -16.126453423 + 9.25

Combine like terms: -9.25 + 9.25 = 0.00
0.00 + t = -16.126453423 + 9.25
t = -16.126453423 + 9.25

Combine like terms: -16.126453423 + 9.25 = -6.876453423
t = -6.876453423

Simplifying
t = -6.876453423


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {25.376453423, -6.876453423}

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