(4.9t^2)-(.77t)-(.11)=0

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Solution for (4.9t^2)-(.77t)-(.11)=0 equation:


Simplifying
(4.9t2) + -1(0.77t) + -1(0.11) = 0

Remove parenthesis around (0.77t)
(4.9t2) + -1 * 0.77t + -1(0.11) = 0

Multiply -1 * 0.77
(4.9t2) + -0.77t + -1(0.11) = 0

Multiply -1 * 0.11
(4.9t2) + -0.77t + -0.11 = 0

Reorder the terms:
-0.11 + -0.77t + (4.9t2) = 0

Solving
-0.11 + -0.77t + (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'.
-0.02244897959 + -0.1571428571t + t2 = 0

Move the constant term to the right:

Add '0.02244897959' to each side of the equation.
-0.02244897959 + -0.1571428571t + 0.02244897959 + t2 = 0 + 0.02244897959

Reorder the terms:
-0.02244897959 + 0.02244897959 + -0.1571428571t + t2 = 0 + 0.02244897959

Combine like terms: -0.02244897959 + 0.02244897959 = 0.00000000000
0.00000000000 + -0.1571428571t + t2 = 0 + 0.02244897959
-0.1571428571t + t2 = 0 + 0.02244897959

Combine like terms: 0 + 0.02244897959 = 0.02244897959
-0.1571428571t + t2 = 0.02244897959

The t term is -0.1571428571t.  Take half its coefficient (-0.07857142855).
Square it (0.006173469384) and add it to both sides.

Add '0.006173469384' to each side of the equation.
-0.1571428571t + 0.006173469384 + t2 = 0.02244897959 + 0.006173469384

Reorder the terms:
0.006173469384 + -0.1571428571t + t2 = 0.02244897959 + 0.006173469384

Combine like terms: 0.02244897959 + 0.006173469384 = 0.028622448974
0.006173469384 + -0.1571428571t + t2 = 0.028622448974

Factor a perfect square on the left side:
((t) + -0.07857142855)((t) + -0.07857142855) = 0.028622448974

Calculate the square root of the right side: 0.169181704

Break this problem into two subproblems by setting 
((t) + -0.07857142855) equal to 0.169181704 and -0.169181704.

Subproblem 1

(t) + -0.07857142855 = 0.169181704 Simplifying (t) + -0.07857142855 = 0.169181704 t + -0.07857142855 = 0.169181704 Reorder the terms: -0.07857142855 + t = 0.169181704 Solving -0.07857142855 + t = 0.169181704 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.07857142855' to each side of the equation. -0.07857142855 + 0.07857142855 + t = 0.169181704 + 0.07857142855 Combine like terms: -0.07857142855 + 0.07857142855 = 0.00000000000 0.00000000000 + t = 0.169181704 + 0.07857142855 t = 0.169181704 + 0.07857142855 Combine like terms: 0.169181704 + 0.07857142855 = 0.24775313255 t = 0.24775313255 Simplifying t = 0.24775313255

Subproblem 2

(t) + -0.07857142855 = -0.169181704 Simplifying (t) + -0.07857142855 = -0.169181704 t + -0.07857142855 = -0.169181704 Reorder the terms: -0.07857142855 + t = -0.169181704 Solving -0.07857142855 + t = -0.169181704 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.07857142855' to each side of the equation. -0.07857142855 + 0.07857142855 + t = -0.169181704 + 0.07857142855 Combine like terms: -0.07857142855 + 0.07857142855 = 0.00000000000 0.00000000000 + t = -0.169181704 + 0.07857142855 t = -0.169181704 + 0.07857142855 Combine like terms: -0.169181704 + 0.07857142855 = -0.09061027545 t = -0.09061027545 Simplifying t = -0.09061027545

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.24775313255, -0.09061027545}

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