-4.9t^2+5.5t+12=0

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Solution for -4.9t^2+5.5t+12=0 equation:


Simplifying
-4.9t2 + 5.5t + 12 = 0

Reorder the terms:
12 + 5.5t + -4.9t2 = 0

Solving
12 + 5.5t + -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'.
-2.448979592 + -1.12244898t + t2 = 0

Move the constant term to the right:

Add '2.448979592' to each side of the equation.
-2.448979592 + -1.12244898t + 2.448979592 + t2 = 0 + 2.448979592

Reorder the terms:
-2.448979592 + 2.448979592 + -1.12244898t + t2 = 0 + 2.448979592

Combine like terms: -2.448979592 + 2.448979592 = 0.000000000
0.000000000 + -1.12244898t + t2 = 0 + 2.448979592
-1.12244898t + t2 = 0 + 2.448979592

Combine like terms: 0 + 2.448979592 = 2.448979592
-1.12244898t + t2 = 2.448979592

The t term is -1.12244898t.  Take half its coefficient (-0.56122449).
Square it (0.3149729282) and add it to both sides.

Add '0.3149729282' to each side of the equation.
-1.12244898t + 0.3149729282 + t2 = 2.448979592 + 0.3149729282

Reorder the terms:
0.3149729282 + -1.12244898t + t2 = 2.448979592 + 0.3149729282

Combine like terms: 2.448979592 + 0.3149729282 = 2.7639525202
0.3149729282 + -1.12244898t + t2 = 2.7639525202

Factor a perfect square on the left side:
(t + -0.56122449)(t + -0.56122449) = 2.7639525202

Calculate the square root of the right side: 1.662513916

Break this problem into two subproblems by setting 
(t + -0.56122449) equal to 1.662513916 and -1.662513916.

Subproblem 1

t + -0.56122449 = 1.662513916 Simplifying t + -0.56122449 = 1.662513916 Reorder the terms: -0.56122449 + t = 1.662513916 Solving -0.56122449 + t = 1.662513916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = 1.662513916 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = 1.662513916 + 0.56122449 t = 1.662513916 + 0.56122449 Combine like terms: 1.662513916 + 0.56122449 = 2.223738406 t = 2.223738406 Simplifying t = 2.223738406

Subproblem 2

t + -0.56122449 = -1.662513916 Simplifying t + -0.56122449 = -1.662513916 Reorder the terms: -0.56122449 + t = -1.662513916 Solving -0.56122449 + t = -1.662513916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = -1.662513916 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = -1.662513916 + 0.56122449 t = -1.662513916 + 0.56122449 Combine like terms: -1.662513916 + 0.56122449 = -1.101289426 t = -1.101289426 Simplifying t = -1.101289426

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.223738406, -1.101289426}

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