4.9t^2+225t-620=0

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Solution for 4.9t^2+225t-620=0 equation: 


Simplifying
4.9t2 + 225t + -620 = 0

Reorder the terms:
-620 + 225t + 4.9t2 = 0

Solving
-620 + 225t + 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'.
-126.5306122 + 45.91836735t + t2 = 0

Move the constant term to the right:

Add '126.5306122' to each side of the equation.
-126.5306122 + 45.91836735t + 126.5306122 + t2 = 0 + 126.5306122

Reorder the terms:
-126.5306122 + 126.5306122 + 45.91836735t + t2 = 0 + 126.5306122

Combine like terms: -126.5306122 + 126.5306122 = 0.0000000
0.0000000 + 45.91836735t + t2 = 0 + 126.5306122
45.91836735t + t2 = 0 + 126.5306122

Combine like terms: 0 + 126.5306122 = 126.5306122
45.91836735t + t2 = 126.5306122

The t term is 45.91836735t.  Take half its coefficient (22.95918368).
Square it (527.1241153) and add it to both sides.

Add '527.1241153' to each side of the equation.
45.91836735t + 527.1241153 + t2 = 126.5306122 + 527.1241153

Reorder the terms:
527.1241153 + 45.91836735t + t2 = 126.5306122 + 527.1241153

Combine like terms: 126.5306122 + 527.1241153 = 653.6547275
527.1241153 + 45.91836735t + t2 = 653.6547275

Factor a perfect square on the left side:
(t + 22.95918368)(t + 22.95918368) = 653.6547275

Calculate the square root of the right side: 25.566672202

Break this problem into two subproblems by setting 
(t + 22.95918368) equal to 25.566672202 and -25.566672202.


Subproblem 1
t + 22.95918368 = 25.566672202

Simplifying
t + 22.95918368 = 25.566672202

Reorder the terms:
22.95918368 + t = 25.566672202

Solving
22.95918368 + t = 25.566672202

Solving for variable 't'.

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

Add '-22.95918368' to each side of the equation.
22.95918368 + -22.95918368 + t = 25.566672202 + -22.95918368

Combine like terms: 22.95918368 + -22.95918368 = 0.00000000
0.00000000 + t = 25.566672202 + -22.95918368
t = 25.566672202 + -22.95918368

Combine like terms: 25.566672202 + -22.95918368 = 2.607488522
t = 2.607488522

Simplifying
t = 2.607488522


Subproblem 2
t + 22.95918368 = -25.566672202

Simplifying
t + 22.95918368 = -25.566672202

Reorder the terms:
22.95918368 + t = -25.566672202

Solving
22.95918368 + t = -25.566672202

Solving for variable 't'.

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

Add '-22.95918368' to each side of the equation.
22.95918368 + -22.95918368 + t = -25.566672202 + -22.95918368

Combine like terms: 22.95918368 + -22.95918368 = 0.00000000
0.00000000 + t = -25.566672202 + -22.95918368
t = -25.566672202 + -22.95918368

Combine like terms: -25.566672202 + -22.95918368 = -48.525855882
t = -48.525855882

Simplifying
t = -48.525855882


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.607488522, -48.525855882}

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