4.9t^2+21t-36.5=0

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Solution for 4.9t^2+21t-36.5=0 equation: 


Simplifying
4.9t2 + 21t + -36.5 = 0

Reorder the terms:
-36.5 + 21t + 4.9t2 = 0

Solving
-36.5 + 21t + 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'.
-7.448979592 + 4.285714286t + t2 = 0

Move the constant term to the right:

Add '7.448979592' to each side of the equation.
-7.448979592 + 4.285714286t + 7.448979592 + t2 = 0 + 7.448979592

Reorder the terms:
-7.448979592 + 7.448979592 + 4.285714286t + t2 = 0 + 7.448979592

Combine like terms: -7.448979592 + 7.448979592 = 0.000000000
0.000000000 + 4.285714286t + t2 = 0 + 7.448979592
4.285714286t + t2 = 0 + 7.448979592

Combine like terms: 0 + 7.448979592 = 7.448979592
4.285714286t + t2 = 7.448979592

The t term is 4.285714286t.  Take half its coefficient (2.142857143).
Square it (4.591836735) and add it to both sides.

Add '4.591836735' to each side of the equation.
4.285714286t + 4.591836735 + t2 = 7.448979592 + 4.591836735

Reorder the terms:
4.591836735 + 4.285714286t + t2 = 7.448979592 + 4.591836735

Combine like terms: 7.448979592 + 4.591836735 = 12.040816327
4.591836735 + 4.285714286t + t2 = 12.040816327

Factor a perfect square on the left side:
(t + 2.142857143)(t + 2.142857143) = 12.040816327

Calculate the square root of the right side: 3.469987943

Break this problem into two subproblems by setting 
(t + 2.142857143) equal to 3.469987943 and -3.469987943.


Subproblem 1
t + 2.142857143 = 3.469987943

Simplifying
t + 2.142857143 = 3.469987943

Reorder the terms:
2.142857143 + t = 3.469987943

Solving
2.142857143 + t = 3.469987943

Solving for variable 't'.

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

Add '-2.142857143' to each side of the equation.
2.142857143 + -2.142857143 + t = 3.469987943 + -2.142857143

Combine like terms: 2.142857143 + -2.142857143 = 0.000000000
0.000000000 + t = 3.469987943 + -2.142857143
t = 3.469987943 + -2.142857143

Combine like terms: 3.469987943 + -2.142857143 = 1.3271308
t = 1.3271308

Simplifying
t = 1.3271308


Subproblem 2
t + 2.142857143 = -3.469987943

Simplifying
t + 2.142857143 = -3.469987943

Reorder the terms:
2.142857143 + t = -3.469987943

Solving
2.142857143 + t = -3.469987943

Solving for variable 't'.

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

Add '-2.142857143' to each side of the equation.
2.142857143 + -2.142857143 + t = -3.469987943 + -2.142857143

Combine like terms: 2.142857143 + -2.142857143 = 0.000000000
0.000000000 + t = -3.469987943 + -2.142857143
t = -3.469987943 + -2.142857143

Combine like terms: -3.469987943 + -2.142857143 = -5.612845086
t = -5.612845086

Simplifying
t = -5.612845086


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.3271308, -5.612845086}

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