-5t^2+47t-27=0

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Solution for -5t^2+47t-27=0 equation: 


Simplifying
-5t2 + 47t + -27 = 0

Reorder the terms:
-27 + 47t + -5t2 = 0

Solving
-27 + 47t + -5t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
5.4 + -9.4t + t2 = 0

Move the constant term to the right:

Add '-5.4' to each side of the equation.
5.4 + -9.4t + -5.4 + t2 = 0 + -5.4

Reorder the terms:
5.4 + -5.4 + -9.4t + t2 = 0 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + -9.4t + t2 = 0 + -5.4
-9.4t + t2 = 0 + -5.4

Combine like terms: 0 + -5.4 = -5.4
-9.4t + t2 = -5.4

The t term is -9.4t.  Take half its coefficient (-4.7).
Square it (22.09) and add it to both sides.

Add '22.09' to each side of the equation.
-9.4t + 22.09 + t2 = -5.4 + 22.09

Reorder the terms:
22.09 + -9.4t + t2 = -5.4 + 22.09

Combine like terms: -5.4 + 22.09 = 16.69
22.09 + -9.4t + t2 = 16.69

Factor a perfect square on the left side:
(t + -4.7)(t + -4.7) = 16.69

Calculate the square root of the right side: 4.085339643

Break this problem into two subproblems by setting 
(t + -4.7) equal to 4.085339643 and -4.085339643.


Subproblem 1
t + -4.7 = 4.085339643

Simplifying
t + -4.7 = 4.085339643

Reorder the terms:
-4.7 + t = 4.085339643

Solving
-4.7 + t = 4.085339643

Solving for variable 't'.

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

Add '4.7' to each side of the equation.
-4.7 + 4.7 + t = 4.085339643 + 4.7

Combine like terms: -4.7 + 4.7 = 0.0
0.0 + t = 4.085339643 + 4.7
t = 4.085339643 + 4.7

Combine like terms: 4.085339643 + 4.7 = 8.785339643
t = 8.785339643

Simplifying
t = 8.785339643


Subproblem 2
t + -4.7 = -4.085339643

Simplifying
t + -4.7 = -4.085339643

Reorder the terms:
-4.7 + t = -4.085339643

Solving
-4.7 + t = -4.085339643

Solving for variable 't'.

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

Add '4.7' to each side of the equation.
-4.7 + 4.7 + t = -4.085339643 + 4.7

Combine like terms: -4.7 + 4.7 = 0.0
0.0 + t = -4.085339643 + 4.7
t = -4.085339643 + 4.7

Combine like terms: -4.085339643 + 4.7 = 0.614660357
t = 0.614660357

Simplifying
t = 0.614660357


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.785339643, 0.614660357}

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