4.9(t^2)+11-17.62t=0

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Solution for 4.9(t^2)+11-17.62t=0 equation:


Simplifying
4.9(t2) + 11 + -17.62t = 0

Reorder the terms:
11 + -17.62t + 4.9t2 = 0

Solving
11 + -17.62t + 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'.
2.244897959 + -3.595918367t + t2 = 0

Move the constant term to the right:

Add '-2.244897959' to each side of the equation.
2.244897959 + -3.595918367t + -2.244897959 + t2 = 0 + -2.244897959

Reorder the terms:
2.244897959 + -2.244897959 + -3.595918367t + t2 = 0 + -2.244897959

Combine like terms: 2.244897959 + -2.244897959 = 0.000000000
0.000000000 + -3.595918367t + t2 = 0 + -2.244897959
-3.595918367t + t2 = 0 + -2.244897959

Combine like terms: 0 + -2.244897959 = -2.244897959
-3.595918367t + t2 = -2.244897959

The t term is -3.595918367t.  Take half its coefficient (-1.797959184).
Square it (3.232657227) and add it to both sides.

Add '3.232657227' to each side of the equation.
-3.595918367t + 3.232657227 + t2 = -2.244897959 + 3.232657227

Reorder the terms:
3.232657227 + -3.595918367t + t2 = -2.244897959 + 3.232657227

Combine like terms: -2.244897959 + 3.232657227 = 0.987759268
3.232657227 + -3.595918367t + t2 = 0.987759268

Factor a perfect square on the left side:
(t + -1.797959184)(t + -1.797959184) = 0.987759268

Calculate the square root of the right side: 0.993860789

Break this problem into two subproblems by setting 
(t + -1.797959184) equal to 0.993860789 and -0.993860789.

Subproblem 1

t + -1.797959184 = 0.993860789 Simplifying t + -1.797959184 = 0.993860789 Reorder the terms: -1.797959184 + t = 0.993860789 Solving -1.797959184 + t = 0.993860789 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.797959184' to each side of the equation. -1.797959184 + 1.797959184 + t = 0.993860789 + 1.797959184 Combine like terms: -1.797959184 + 1.797959184 = 0.000000000 0.000000000 + t = 0.993860789 + 1.797959184 t = 0.993860789 + 1.797959184 Combine like terms: 0.993860789 + 1.797959184 = 2.791819973 t = 2.791819973 Simplifying t = 2.791819973

Subproblem 2

t + -1.797959184 = -0.993860789 Simplifying t + -1.797959184 = -0.993860789 Reorder the terms: -1.797959184 + t = -0.993860789 Solving -1.797959184 + t = -0.993860789 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.797959184' to each side of the equation. -1.797959184 + 1.797959184 + t = -0.993860789 + 1.797959184 Combine like terms: -1.797959184 + 1.797959184 = 0.000000000 0.000000000 + t = -0.993860789 + 1.797959184 t = -0.993860789 + 1.797959184 Combine like terms: -0.993860789 + 1.797959184 = 0.804098395 t = 0.804098395 Simplifying t = 0.804098395

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.791819973, 0.804098395}

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