0=1.2t^2-17.68t+4.8

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Solution for 0=1.2t^2-17.68t+4.8 equation:


Simplifying
0 = 1.2t2 + -17.68t + 4.8

Reorder the terms:
0 = 4.8 + -17.68t + 1.2t2

Solving
0 = 4.8 + -17.68t + 1.2t2

Solving for variable 't'.

Combine like terms: 0 + -4.8 = -4.8
-4.8 + 17.68t + -1.2t2 = 4.8 + -17.68t + 1.2t2 + -4.8 + 17.68t + -1.2t2

Reorder the terms:
-4.8 + 17.68t + -1.2t2 = 4.8 + -4.8 + -17.68t + 17.68t + 1.2t2 + -1.2t2

Combine like terms: 4.8 + -4.8 = 0.0
-4.8 + 17.68t + -1.2t2 = 0.0 + -17.68t + 17.68t + 1.2t2 + -1.2t2
-4.8 + 17.68t + -1.2t2 = -17.68t + 17.68t + 1.2t2 + -1.2t2

Combine like terms: -17.68t + 17.68t = 0.00
-4.8 + 17.68t + -1.2t2 = 0.00 + 1.2t2 + -1.2t2
-4.8 + 17.68t + -1.2t2 = 1.2t2 + -1.2t2

Combine like terms: 1.2t2 + -1.2t2 = 0.0
-4.8 + 17.68t + -1.2t2 = 0.0

Begin completing the square.  Divide all terms by
-1.2 the coefficient of the squared term: 

Divide each side by '-1.2'.
4 + -14.73333333t + t2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -14.73333333t + -4 + t2 = 0 + -4

Reorder the terms:
4 + -4 + -14.73333333t + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -14.73333333t + t2 = 0 + -4
-14.73333333t + t2 = 0 + -4

Combine like terms: 0 + -4 = -4
-14.73333333t + t2 = -4

The t term is -14.73333333t.  Take half its coefficient (-7.366666665).
Square it (54.26777775) and add it to both sides.

Add '54.26777775' to each side of the equation.
-14.73333333t + 54.26777775 + t2 = -4 + 54.26777775

Reorder the terms:
54.26777775 + -14.73333333t + t2 = -4 + 54.26777775

Combine like terms: -4 + 54.26777775 = 50.26777775
54.26777775 + -14.73333333t + t2 = 50.26777775

Factor a perfect square on the left side:
(t + -7.366666665)(t + -7.366666665) = 50.26777775

Calculate the square root of the right side: 7.089977274

Break this problem into two subproblems by setting 
(t + -7.366666665) equal to 7.089977274 and -7.089977274.

Subproblem 1

t + -7.366666665 = 7.089977274 Simplifying t + -7.366666665 = 7.089977274 Reorder the terms: -7.366666665 + t = 7.089977274 Solving -7.366666665 + t = 7.089977274 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.366666665' to each side of the equation. -7.366666665 + 7.366666665 + t = 7.089977274 + 7.366666665 Combine like terms: -7.366666665 + 7.366666665 = 0.000000000 0.000000000 + t = 7.089977274 + 7.366666665 t = 7.089977274 + 7.366666665 Combine like terms: 7.089977274 + 7.366666665 = 14.456643939 t = 14.456643939 Simplifying t = 14.456643939

Subproblem 2

t + -7.366666665 = -7.089977274 Simplifying t + -7.366666665 = -7.089977274 Reorder the terms: -7.366666665 + t = -7.089977274 Solving -7.366666665 + t = -7.089977274 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.366666665' to each side of the equation. -7.366666665 + 7.366666665 + t = -7.089977274 + 7.366666665 Combine like terms: -7.366666665 + 7.366666665 = 0.000000000 0.000000000 + t = -7.089977274 + 7.366666665 t = -7.089977274 + 7.366666665 Combine like terms: -7.089977274 + 7.366666665 = 0.276689391 t = 0.276689391 Simplifying t = 0.276689391

Solution

The solution to the problem is based on the solutions from the subproblems. t = {14.456643939, 0.276689391}

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