-2.78t^2+25t-30=0

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Solution for -2.78t^2+25t-30=0 equation: 


Simplifying
-2.78t2 + 25t + -30 = 0

Reorder the terms:
-30 + 25t + -2.78t2 = 0

Solving
-30 + 25t + -2.78t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-2.78 the coefficient of the squared term: 

Divide each side by '-2.78'.
10.79136691 + -8.992805755t + t2 = 0

Move the constant term to the right:

Add '-10.79136691' to each side of the equation.
10.79136691 + -8.992805755t + -10.79136691 + t2 = 0 + -10.79136691

Reorder the terms:
10.79136691 + -10.79136691 + -8.992805755t + t2 = 0 + -10.79136691

Combine like terms: 10.79136691 + -10.79136691 = 0.00000000
0.00000000 + -8.992805755t + t2 = 0 + -10.79136691
-8.992805755t + t2 = 0 + -10.79136691

Combine like terms: 0 + -10.79136691 = -10.79136691
-8.992805755t + t2 = -10.79136691

The t term is -8.992805755t.  Take half its coefficient (-4.496402878).
Square it (20.21763884) and add it to both sides.

Add '20.21763884' to each side of the equation.
-8.992805755t + 20.21763884 + t2 = -10.79136691 + 20.21763884

Reorder the terms:
20.21763884 + -8.992805755t + t2 = -10.79136691 + 20.21763884

Combine like terms: -10.79136691 + 20.21763884 = 9.42627193
20.21763884 + -8.992805755t + t2 = 9.42627193

Factor a perfect square on the left side:
(t + -4.496402878)(t + -4.496402878) = 9.42627193

Calculate the square root of the right side: 3.070223433

Break this problem into two subproblems by setting 
(t + -4.496402878) equal to 3.070223433 and -3.070223433.


Subproblem 1
t + -4.496402878 = 3.070223433

Simplifying
t + -4.496402878 = 3.070223433

Reorder the terms:
-4.496402878 + t = 3.070223433

Solving
-4.496402878 + t = 3.070223433

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '4.496402878' to each side of the equation.
-4.496402878 + 4.496402878 + t = 3.070223433 + 4.496402878

Combine like terms: -4.496402878 + 4.496402878 = 0.000000000
0.000000000 + t = 3.070223433 + 4.496402878
t = 3.070223433 + 4.496402878

Combine like terms: 3.070223433 + 4.496402878 = 7.566626311
t = 7.566626311

Simplifying
t = 7.566626311


Subproblem 2
t + -4.496402878 = -3.070223433

Simplifying
t + -4.496402878 = -3.070223433

Reorder the terms:
-4.496402878 + t = -3.070223433

Solving
-4.496402878 + t = -3.070223433

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '4.496402878' to each side of the equation.
-4.496402878 + 4.496402878 + t = -3.070223433 + 4.496402878

Combine like terms: -4.496402878 + 4.496402878 = 0.000000000
0.000000000 + t = -3.070223433 + 4.496402878
t = -3.070223433 + 4.496402878

Combine like terms: -3.070223433 + 4.496402878 = 1.426179445
t = 1.426179445

Simplifying
t = 1.426179445


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.566626311, 1.426179445}

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