4.9t^2+19t-41=0

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Solution for 4.9t^2+19t-41=0 equation:


Simplifying
4.9t2 + 19t + -41 = 0

Reorder the terms:
-41 + 19t + 4.9t2 = 0

Solving
-41 + 19t + 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'.
-8.367346939 + 3.87755102t + t2 = 0

Move the constant term to the right:

Add '8.367346939' to each side of the equation.
-8.367346939 + 3.87755102t + 8.367346939 + t2 = 0 + 8.367346939

Reorder the terms:
-8.367346939 + 8.367346939 + 3.87755102t + t2 = 0 + 8.367346939

Combine like terms: -8.367346939 + 8.367346939 = 0.000000000
0.000000000 + 3.87755102t + t2 = 0 + 8.367346939
3.87755102t + t2 = 0 + 8.367346939

Combine like terms: 0 + 8.367346939 = 8.367346939
3.87755102t + t2 = 8.367346939

The t term is 3.87755102t.  Take half its coefficient (1.93877551).
Square it (3.758850478) and add it to both sides.

Add '3.758850478' to each side of the equation.
3.87755102t + 3.758850478 + t2 = 8.367346939 + 3.758850478

Reorder the terms:
3.758850478 + 3.87755102t + t2 = 8.367346939 + 3.758850478

Combine like terms: 8.367346939 + 3.758850478 = 12.126197417
3.758850478 + 3.87755102t + t2 = 12.126197417

Factor a perfect square on the left side:
(t + 1.93877551)(t + 1.93877551) = 12.126197417

Calculate the square root of the right side: 3.482269004

Break this problem into two subproblems by setting 
(t + 1.93877551) equal to 3.482269004 and -3.482269004.

Subproblem 1

t + 1.93877551 = 3.482269004 Simplifying t + 1.93877551 = 3.482269004 Reorder the terms: 1.93877551 + t = 3.482269004 Solving 1.93877551 + t = 3.482269004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.93877551' to each side of the equation. 1.93877551 + -1.93877551 + t = 3.482269004 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + t = 3.482269004 + -1.93877551 t = 3.482269004 + -1.93877551 Combine like terms: 3.482269004 + -1.93877551 = 1.543493494 t = 1.543493494 Simplifying t = 1.543493494

Subproblem 2

t + 1.93877551 = -3.482269004 Simplifying t + 1.93877551 = -3.482269004 Reorder the terms: 1.93877551 + t = -3.482269004 Solving 1.93877551 + t = -3.482269004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.93877551' to each side of the equation. 1.93877551 + -1.93877551 + t = -3.482269004 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + t = -3.482269004 + -1.93877551 t = -3.482269004 + -1.93877551 Combine like terms: -3.482269004 + -1.93877551 = -5.421044514 t = -5.421044514 Simplifying t = -5.421044514

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.543493494, -5.421044514}

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