0=11t^2-130t-190

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Solution for 0=11t^2-130t-190 equation:


Simplifying
0 = 11t2 + -130t + -190

Reorder the terms:
0 = -190 + -130t + 11t2

Solving
0 = -190 + -130t + 11t2

Solving for variable 't'.

Combine like terms: 0 + 190 = 190
190 + 130t + -11t2 = -190 + -130t + 11t2 + 190 + 130t + -11t2

Reorder the terms:
190 + 130t + -11t2 = -190 + 190 + -130t + 130t + 11t2 + -11t2

Combine like terms: -190 + 190 = 0
190 + 130t + -11t2 = 0 + -130t + 130t + 11t2 + -11t2
190 + 130t + -11t2 = -130t + 130t + 11t2 + -11t2

Combine like terms: -130t + 130t = 0
190 + 130t + -11t2 = 0 + 11t2 + -11t2
190 + 130t + -11t2 = 11t2 + -11t2

Combine like terms: 11t2 + -11t2 = 0
190 + 130t + -11t2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-17.27272727 + -11.81818182t + t2 = 0

Move the constant term to the right:

Add '17.27272727' to each side of the equation.
-17.27272727 + -11.81818182t + 17.27272727 + t2 = 0 + 17.27272727

Reorder the terms:
-17.27272727 + 17.27272727 + -11.81818182t + t2 = 0 + 17.27272727

Combine like terms: -17.27272727 + 17.27272727 = 0.00000000
0.00000000 + -11.81818182t + t2 = 0 + 17.27272727
-11.81818182t + t2 = 0 + 17.27272727

Combine like terms: 0 + 17.27272727 = 17.27272727
-11.81818182t + t2 = 17.27272727

The t term is -11.81818182t.  Take half its coefficient (-5.90909091).
Square it (34.91735538) and add it to both sides.

Add '34.91735538' to each side of the equation.
-11.81818182t + 34.91735538 + t2 = 17.27272727 + 34.91735538

Reorder the terms:
34.91735538 + -11.81818182t + t2 = 17.27272727 + 34.91735538

Combine like terms: 17.27272727 + 34.91735538 = 52.19008265
34.91735538 + -11.81818182t + t2 = 52.19008265

Factor a perfect square on the left side:
(t + -5.90909091)(t + -5.90909091) = 52.19008265

Calculate the square root of the right side: 7.224270389

Break this problem into two subproblems by setting 
(t + -5.90909091) equal to 7.224270389 and -7.224270389.

Subproblem 1

t + -5.90909091 = 7.224270389 Simplifying t + -5.90909091 = 7.224270389 Reorder the terms: -5.90909091 + t = 7.224270389 Solving -5.90909091 + t = 7.224270389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.90909091' to each side of the equation. -5.90909091 + 5.90909091 + t = 7.224270389 + 5.90909091 Combine like terms: -5.90909091 + 5.90909091 = 0.00000000 0.00000000 + t = 7.224270389 + 5.90909091 t = 7.224270389 + 5.90909091 Combine like terms: 7.224270389 + 5.90909091 = 13.133361299 t = 13.133361299 Simplifying t = 13.133361299

Subproblem 2

t + -5.90909091 = -7.224270389 Simplifying t + -5.90909091 = -7.224270389 Reorder the terms: -5.90909091 + t = -7.224270389 Solving -5.90909091 + t = -7.224270389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.90909091' to each side of the equation. -5.90909091 + 5.90909091 + t = -7.224270389 + 5.90909091 Combine like terms: -5.90909091 + 5.90909091 = 0.00000000 0.00000000 + t = -7.224270389 + 5.90909091 t = -7.224270389 + 5.90909091 Combine like terms: -7.224270389 + 5.90909091 = -1.315179479 t = -1.315179479 Simplifying t = -1.315179479

Solution

The solution to the problem is based on the solutions from the subproblems. t = {13.133361299, -1.315179479}

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