t^2-5t-30=0

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


Simplifying
t2 + -5t + -30 = 0

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

Solving
-30 + -5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -5t + 30 + t2 = 0 + 30

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

Combine like terms: -30 + 30 = 0
0 + -5t + t2 = 0 + 30
-5t + t2 = 0 + 30

Combine like terms: 0 + 30 = 30
-5t + t2 = 30

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = 30 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 30 + 6.25

Combine like terms: 30 + 6.25 = 36.25
6.25 + -5t + t2 = 36.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(t + -2.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
t + -2.5 = 6.020797289

Simplifying
t + -2.5 = 6.020797289

Reorder the terms:
-2.5 + t = 6.020797289

Solving
-2.5 + t = 6.020797289

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 6.020797289 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 6.020797289 + 2.5
t = 6.020797289 + 2.5

Combine like terms: 6.020797289 + 2.5 = 8.520797289
t = 8.520797289

Simplifying
t = 8.520797289


Subproblem 2
t + -2.5 = -6.020797289

Simplifying
t + -2.5 = -6.020797289

Reorder the terms:
-2.5 + t = -6.020797289

Solving
-2.5 + t = -6.020797289

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -6.020797289 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -6.020797289 + 2.5
t = -6.020797289 + 2.5

Combine like terms: -6.020797289 + 2.5 = -3.520797289
t = -3.520797289

Simplifying
t = -3.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.520797289, -3.520797289}

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