9.8t^2-32t-5.5=0

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Solution for 9.8t^2-32t-5.5=0 equation:


Simplifying
9.8t2 + -32t + -5.5 = 0

Reorder the terms:
-5.5 + -32t + 9.8t2 = 0

Solving
-5.5 + -32t + 9.8t2 = 0

Solving for variable 't'.

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

Divide each side by '9.8'.
-0.5612244898 + -3.265306122t + t2 = 0

Move the constant term to the right:

Add '0.5612244898' to each side of the equation.
-0.5612244898 + -3.265306122t + 0.5612244898 + t2 = 0 + 0.5612244898

Reorder the terms:
-0.5612244898 + 0.5612244898 + -3.265306122t + t2 = 0 + 0.5612244898

Combine like terms: -0.5612244898 + 0.5612244898 = 0.0000000000
0.0000000000 + -3.265306122t + t2 = 0 + 0.5612244898
-3.265306122t + t2 = 0 + 0.5612244898

Combine like terms: 0 + 0.5612244898 = 0.5612244898
-3.265306122t + t2 = 0.5612244898

The t term is -3.265306122t.  Take half its coefficient (-1.632653061).
Square it (2.665556018) and add it to both sides.

Add '2.665556018' to each side of the equation.
-3.265306122t + 2.665556018 + t2 = 0.5612244898 + 2.665556018

Reorder the terms:
2.665556018 + -3.265306122t + t2 = 0.5612244898 + 2.665556018

Combine like terms: 0.5612244898 + 2.665556018 = 3.2267805078
2.665556018 + -3.265306122t + t2 = 3.2267805078

Factor a perfect square on the left side:
(t + -1.632653061)(t + -1.632653061) = 3.2267805078

Calculate the square root of the right side: 1.796324166

Break this problem into two subproblems by setting 
(t + -1.632653061) equal to 1.796324166 and -1.796324166.

Subproblem 1

t + -1.632653061 = 1.796324166 Simplifying t + -1.632653061 = 1.796324166 Reorder the terms: -1.632653061 + t = 1.796324166 Solving -1.632653061 + t = 1.796324166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 1.796324166 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 1.796324166 + 1.632653061 t = 1.796324166 + 1.632653061 Combine like terms: 1.796324166 + 1.632653061 = 3.428977227 t = 3.428977227 Simplifying t = 3.428977227

Subproblem 2

t + -1.632653061 = -1.796324166 Simplifying t + -1.632653061 = -1.796324166 Reorder the terms: -1.632653061 + t = -1.796324166 Solving -1.632653061 + t = -1.796324166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -1.796324166 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -1.796324166 + 1.632653061 t = -1.796324166 + 1.632653061 Combine like terms: -1.796324166 + 1.632653061 = -0.163671105 t = -0.163671105 Simplifying t = -0.163671105

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.428977227, -0.163671105}

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