5t^2-35t-30=0

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Solution for 5t^2-35t-30=0 equation: 


Simplifying
5t2 + -35t + -30 = 0

Reorder the terms:
-30 + -35t + 5t2 = 0

Solving
-30 + -35t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -7t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-6 + -7t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + -7t + t2 = 0

Solving
-6 + -7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -7t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7t + t2 = 0 + 6
-7t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7t + t2 = 6

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 6 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7t + t2 = 18.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(t + -3.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
t + -3.5 = 4.272001873

Simplifying
t + -3.5 = 4.272001873

Reorder the terms:
-3.5 + t = 4.272001873

Solving
-3.5 + t = 4.272001873

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 4.272001873 + 3.5
t = 4.272001873 + 3.5

Combine like terms: 4.272001873 + 3.5 = 7.772001873
t = 7.772001873

Simplifying
t = 7.772001873


Subproblem 2
t + -3.5 = -4.272001873

Simplifying
t + -3.5 = -4.272001873

Reorder the terms:
-3.5 + t = -4.272001873

Solving
-3.5 + t = -4.272001873

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -4.272001873 + 3.5
t = -4.272001873 + 3.5

Combine like terms: -4.272001873 + 3.5 = -0.772001873
t = -0.772001873

Simplifying
t = -0.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.772001873, -0.772001873}
Solution
t = {7.772001873, -0.772001873}

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