4.9t^2+12.5t-21=0

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Solution for 4.9t^2+12.5t-21=0 equation: 


Simplifying
4.9t2 + 12.5t + -21 = 0

Reorder the terms:
-21 + 12.5t + 4.9t2 = 0

Solving
-21 + 12.5t + 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'.
-4.285714286 + 2.551020408t + t2 = 0

Move the constant term to the right:

Add '4.285714286' to each side of the equation.
-4.285714286 + 2.551020408t + 4.285714286 + t2 = 0 + 4.285714286

Reorder the terms:
-4.285714286 + 4.285714286 + 2.551020408t + t2 = 0 + 4.285714286

Combine like terms: -4.285714286 + 4.285714286 = 0.000000000
0.000000000 + 2.551020408t + t2 = 0 + 4.285714286
2.551020408t + t2 = 0 + 4.285714286

Combine like terms: 0 + 4.285714286 = 4.285714286
2.551020408t + t2 = 4.285714286

The t term is 2.551020408t.  Take half its coefficient (1.275510204).
Square it (1.626926281) and add it to both sides.

Add '1.626926281' to each side of the equation.
2.551020408t + 1.626926281 + t2 = 4.285714286 + 1.626926281

Reorder the terms:
1.626926281 + 2.551020408t + t2 = 4.285714286 + 1.626926281

Combine like terms: 4.285714286 + 1.626926281 = 5.912640567
1.626926281 + 2.551020408t + t2 = 5.912640567

Factor a perfect square on the left side:
(t + 1.275510204)(t + 1.275510204) = 5.912640567

Calculate the square root of the right side: 2.431592188

Break this problem into two subproblems by setting 
(t + 1.275510204) equal to 2.431592188 and -2.431592188.


Subproblem 1
t + 1.275510204 = 2.431592188

Simplifying
t + 1.275510204 = 2.431592188

Reorder the terms:
1.275510204 + t = 2.431592188

Solving
1.275510204 + t = 2.431592188

Solving for variable 't'.

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

Add '-1.275510204' to each side of the equation.
1.275510204 + -1.275510204 + t = 2.431592188 + -1.275510204

Combine like terms: 1.275510204 + -1.275510204 = 0.000000000
0.000000000 + t = 2.431592188 + -1.275510204
t = 2.431592188 + -1.275510204

Combine like terms: 2.431592188 + -1.275510204 = 1.156081984
t = 1.156081984

Simplifying
t = 1.156081984


Subproblem 2
t + 1.275510204 = -2.431592188

Simplifying
t + 1.275510204 = -2.431592188

Reorder the terms:
1.275510204 + t = -2.431592188

Solving
1.275510204 + t = -2.431592188

Solving for variable 't'.

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

Add '-1.275510204' to each side of the equation.
1.275510204 + -1.275510204 + t = -2.431592188 + -1.275510204

Combine like terms: 1.275510204 + -1.275510204 = 0.000000000
0.000000000 + t = -2.431592188 + -1.275510204
t = -2.431592188 + -1.275510204

Combine like terms: -2.431592188 + -1.275510204 = -3.707102392
t = -3.707102392

Simplifying
t = -3.707102392


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.156081984, -3.707102392}

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