-4.9t^2+60.4t+27.4=0

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Solution for -4.9t^2+60.4t+27.4=0 equation:


Simplifying
-4.9t2 + 60.4t + 27.4 = 0

Reorder the terms:
27.4 + 60.4t + -4.9t2 = 0

Solving
27.4 + 60.4t + -4.9t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-5.591836735 + -12.32653061t + t2 = 0

Move the constant term to the right:

Add '5.591836735' to each side of the equation.
-5.591836735 + -12.32653061t + 5.591836735 + t2 = 0 + 5.591836735

Reorder the terms:
-5.591836735 + 5.591836735 + -12.32653061t + t2 = 0 + 5.591836735

Combine like terms: -5.591836735 + 5.591836735 = 0.000000000
0.000000000 + -12.32653061t + t2 = 0 + 5.591836735
-12.32653061t + t2 = 0 + 5.591836735

Combine like terms: 0 + 5.591836735 = 5.591836735
-12.32653061t + t2 = 5.591836735

The t term is -12.32653061t.  Take half its coefficient (-6.163265305).
Square it (37.98583922) and add it to both sides.

Add '37.98583922' to each side of the equation.
-12.32653061t + 37.98583922 + t2 = 5.591836735 + 37.98583922

Reorder the terms:
37.98583922 + -12.32653061t + t2 = 5.591836735 + 37.98583922

Combine like terms: 5.591836735 + 37.98583922 = 43.577675955
37.98583922 + -12.32653061t + t2 = 43.577675955

Factor a perfect square on the left side:
(t + -6.163265305)(t + -6.163265305) = 43.577675955

Calculate the square root of the right side: 6.601338952

Break this problem into two subproblems by setting 
(t + -6.163265305) equal to 6.601338952 and -6.601338952.


Subproblem 1
t + -6.163265305 = 6.601338952

Simplifying
t + -6.163265305 = 6.601338952

Reorder the terms:
-6.163265305 + t = 6.601338952

Solving
-6.163265305 + t = 6.601338952

Solving for variable 't'.

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

Add '6.163265305' to each side of the equation.
-6.163265305 + 6.163265305 + t = 6.601338952 + 6.163265305

Combine like terms: -6.163265305 + 6.163265305 = 0.000000000
0.000000000 + t = 6.601338952 + 6.163265305
t = 6.601338952 + 6.163265305

Combine like terms: 6.601338952 + 6.163265305 = 12.764604257
t = 12.764604257

Simplifying
t = 12.764604257


Subproblem 2
t + -6.163265305 = -6.601338952

Simplifying
t + -6.163265305 = -6.601338952

Reorder the terms:
-6.163265305 + t = -6.601338952

Solving
-6.163265305 + t = -6.601338952

Solving for variable 't'.

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

Add '6.163265305' to each side of the equation.
-6.163265305 + 6.163265305 + t = -6.601338952 + 6.163265305

Combine like terms: -6.163265305 + 6.163265305 = 0.000000000
0.000000000 + t = -6.601338952 + 6.163265305
t = -6.601338952 + 6.163265305

Combine like terms: -6.601338952 + 6.163265305 = -0.438073647
t = -0.438073647

Simplifying
t = -0.438073647


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.764604257, -0.438073647}

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