4.905t^2-58.9t+117.8=0

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Solution for 4.905t^2-58.9t+117.8=0 equation: 


Simplifying
4.905t2 + -58.9t + 117.8 = 0

Reorder the terms:
117.8 + -58.9t + 4.905t2 = 0

Solving
117.8 + -58.9t + 4.905t2 = 0

Solving for variable 't'.

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

Divide each side by '4.905'.
24.01630989 + -12.00815494t + t2 = 0

Move the constant term to the right:

Add '-24.01630989' to each side of the equation.
24.01630989 + -12.00815494t + -24.01630989 + t2 = 0 + -24.01630989

Reorder the terms:
24.01630989 + -24.01630989 + -12.00815494t + t2 = 0 + -24.01630989

Combine like terms: 24.01630989 + -24.01630989 = 0.00000000
0.00000000 + -12.00815494t + t2 = 0 + -24.01630989
-12.00815494t + t2 = 0 + -24.01630989

Combine like terms: 0 + -24.01630989 = -24.01630989
-12.00815494t + t2 = -24.01630989

The t term is -12.00815494t.  Take half its coefficient (-6.00407747).
Square it (36.04894627) and add it to both sides.

Add '36.04894627' to each side of the equation.
-12.00815494t + 36.04894627 + t2 = -24.01630989 + 36.04894627

Reorder the terms:
36.04894627 + -12.00815494t + t2 = -24.01630989 + 36.04894627

Combine like terms: -24.01630989 + 36.04894627 = 12.03263638
36.04894627 + -12.00815494t + t2 = 12.03263638

Factor a perfect square on the left side:
(t + -6.00407747)(t + -6.00407747) = 12.03263638

Calculate the square root of the right side: 3.468809072

Break this problem into two subproblems by setting 
(t + -6.00407747) equal to 3.468809072 and -3.468809072.


Subproblem 1
t + -6.00407747 = 3.468809072

Simplifying
t + -6.00407747 = 3.468809072

Reorder the terms:
-6.00407747 + t = 3.468809072

Solving
-6.00407747 + t = 3.468809072

Solving for variable 't'.

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

Add '6.00407747' to each side of the equation.
-6.00407747 + 6.00407747 + t = 3.468809072 + 6.00407747

Combine like terms: -6.00407747 + 6.00407747 = 0.00000000
0.00000000 + t = 3.468809072 + 6.00407747
t = 3.468809072 + 6.00407747

Combine like terms: 3.468809072 + 6.00407747 = 9.472886542
t = 9.472886542

Simplifying
t = 9.472886542


Subproblem 2
t + -6.00407747 = -3.468809072

Simplifying
t + -6.00407747 = -3.468809072

Reorder the terms:
-6.00407747 + t = -3.468809072

Solving
-6.00407747 + t = -3.468809072

Solving for variable 't'.

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

Add '6.00407747' to each side of the equation.
-6.00407747 + 6.00407747 + t = -3.468809072 + 6.00407747

Combine like terms: -6.00407747 + 6.00407747 = 0.00000000
0.00000000 + t = -3.468809072 + 6.00407747
t = -3.468809072 + 6.00407747

Combine like terms: -3.468809072 + 6.00407747 = 2.535268398
t = 2.535268398

Simplifying
t = 2.535268398


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.472886542, 2.535268398}

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