19.2672t^2-99.408t+124.58=0

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Solution for 19.2672t^2-99.408t+124.58=0 equation: 


Simplifying
19.2672t2 + -99.408t + 124.58 = 0

Reorder the terms:
124.58 + -99.408t + 19.2672t2 = 0

Solving
124.58 + -99.408t + 19.2672t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
19.2672 the coefficient of the squared term: 

Divide each side by '19.2672'.
6.465910978 + -5.159441953t + t2 = 0

Move the constant term to the right:

Add '-6.465910978' to each side of the equation.
6.465910978 + -5.159441953t + -6.465910978 + t2 = 0 + -6.465910978

Reorder the terms:
6.465910978 + -6.465910978 + -5.159441953t + t2 = 0 + -6.465910978

Combine like terms: 6.465910978 + -6.465910978 = 0.000000000
0.000000000 + -5.159441953t + t2 = 0 + -6.465910978
-5.159441953t + t2 = 0 + -6.465910978

Combine like terms: 0 + -6.465910978 = -6.465910978
-5.159441953t + t2 = -6.465910978

The t term is -5.159441953t.  Take half its coefficient (-2.579720977).
Square it (6.654960319) and add it to both sides.

Add '6.654960319' to each side of the equation.
-5.159441953t + 6.654960319 + t2 = -6.465910978 + 6.654960319

Reorder the terms:
6.654960319 + -5.159441953t + t2 = -6.465910978 + 6.654960319

Combine like terms: -6.465910978 + 6.654960319 = 0.189049341
6.654960319 + -5.159441953t + t2 = 0.189049341

Factor a perfect square on the left side:
(t + -2.579720977)(t + -2.579720977) = 0.189049341

Calculate the square root of the right side: 0.434798046

Break this problem into two subproblems by setting 
(t + -2.579720977) equal to 0.434798046 and -0.434798046.


Subproblem 1
t + -2.579720977 = 0.434798046

Simplifying
t + -2.579720977 = 0.434798046

Reorder the terms:
-2.579720977 + t = 0.434798046

Solving
-2.579720977 + t = 0.434798046

Solving for variable 't'.

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

Add '2.579720977' to each side of the equation.
-2.579720977 + 2.579720977 + t = 0.434798046 + 2.579720977

Combine like terms: -2.579720977 + 2.579720977 = 0.000000000
0.000000000 + t = 0.434798046 + 2.579720977
t = 0.434798046 + 2.579720977

Combine like terms: 0.434798046 + 2.579720977 = 3.014519023
t = 3.014519023

Simplifying
t = 3.014519023


Subproblem 2
t + -2.579720977 = -0.434798046

Simplifying
t + -2.579720977 = -0.434798046

Reorder the terms:
-2.579720977 + t = -0.434798046

Solving
-2.579720977 + t = -0.434798046

Solving for variable 't'.

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

Add '2.579720977' to each side of the equation.
-2.579720977 + 2.579720977 + t = -0.434798046 + 2.579720977

Combine like terms: -2.579720977 + 2.579720977 = 0.000000000
0.000000000 + t = -0.434798046 + 2.579720977
t = -0.434798046 + 2.579720977

Combine like terms: -0.434798046 + 2.579720977 = 2.144922931
t = 2.144922931

Simplifying
t = 2.144922931


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.014519023, 2.144922931}

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