3t^2-38.89t=77.78

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Solution for 3t^2-38.89t=77.78 equation:


Simplifying
3t2 + -38.89t = 77.78

Reorder the terms:
-38.89t + 3t2 = 77.78

Solving
-38.89t + 3t2 = 77.78

Solving for variable 't'.

Reorder the terms:
-77.78 + -38.89t + 3t2 = 77.78 + -77.78

Combine like terms: 77.78 + -77.78 = 0.00
-77.78 + -38.89t + 3t2 = 0.00

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

Divide each side by '3'.
-25.92666667 + -12.96333333t + t2 = 0.00

Move the constant term to the right:

Add '25.92666667' to each side of the equation.
-25.92666667 + -12.96333333t + 25.92666667 + t2 = 0.00 + 25.92666667

Reorder the terms:
-25.92666667 + 25.92666667 + -12.96333333t + t2 = 0.00 + 25.92666667

Combine like terms: -25.92666667 + 25.92666667 = 0.00000000
0.00000000 + -12.96333333t + t2 = 0.00 + 25.92666667
-12.96333333t + t2 = 0.00 + 25.92666667

Combine like terms: 0.00 + 25.92666667 = 25.92666667
-12.96333333t + t2 = 25.92666667

The t term is -12.96333333t.  Take half its coefficient (-6.481666665).
Square it (42.01200276) and add it to both sides.

Add '42.01200276' to each side of the equation.
-12.96333333t + 42.01200276 + t2 = 25.92666667 + 42.01200276

Reorder the terms:
42.01200276 + -12.96333333t + t2 = 25.92666667 + 42.01200276

Combine like terms: 25.92666667 + 42.01200276 = 67.93866943
42.01200276 + -12.96333333t + t2 = 67.93866943

Factor a perfect square on the left side:
(t + -6.481666665)(t + -6.481666665) = 67.93866943

Calculate the square root of the right side: 8.2424917

Break this problem into two subproblems by setting 
(t + -6.481666665) equal to 8.2424917 and -8.2424917.

Subproblem 1

t + -6.481666665 = 8.2424917 Simplifying t + -6.481666665 = 8.2424917 Reorder the terms: -6.481666665 + t = 8.2424917 Solving -6.481666665 + t = 8.2424917 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.481666665' to each side of the equation. -6.481666665 + 6.481666665 + t = 8.2424917 + 6.481666665 Combine like terms: -6.481666665 + 6.481666665 = 0.000000000 0.000000000 + t = 8.2424917 + 6.481666665 t = 8.2424917 + 6.481666665 Combine like terms: 8.2424917 + 6.481666665 = 14.724158365 t = 14.724158365 Simplifying t = 14.724158365

Subproblem 2

t + -6.481666665 = -8.2424917 Simplifying t + -6.481666665 = -8.2424917 Reorder the terms: -6.481666665 + t = -8.2424917 Solving -6.481666665 + t = -8.2424917 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.481666665' to each side of the equation. -6.481666665 + 6.481666665 + t = -8.2424917 + 6.481666665 Combine like terms: -6.481666665 + 6.481666665 = 0.000000000 0.000000000 + t = -8.2424917 + 6.481666665 t = -8.2424917 + 6.481666665 Combine like terms: -8.2424917 + 6.481666665 = -1.760825035 t = -1.760825035 Simplifying t = -1.760825035

Solution

The solution to the problem is based on the solutions from the subproblems. t = {14.724158365, -1.760825035}

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