t(t-5)=34

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Solution for t(t-5)=34 equation: 


Simplifying
t(t + -5) = 34

Reorder the terms:
t(-5 + t) = 34
(-5 * t + t * t) = 34
(-5t + t2) = 34

Solving
-5t + t2 = 34

Solving for variable 't'.

Reorder the terms:
-34 + -5t + t2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + -5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -5t + 34 + t2 = 0 + 34

Reorder the terms:
-34 + 34 + -5t + t2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -5t + t2 = 0 + 34
-5t + t2 = 0 + 34

Combine like terms: 0 + 34 = 34
-5t + t2 = 34

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 = 34 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 34 + 6.25

Combine like terms: 34 + 6.25 = 40.25
6.25 + -5t + t2 = 40.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(t + -2.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
t + -2.5 = 6.34428877

Simplifying
t + -2.5 = 6.34428877

Reorder the terms:
-2.5 + t = 6.34428877

Solving
-2.5 + t = 6.34428877

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 = 6.34428877 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 6.34428877 + 2.5
t = 6.34428877 + 2.5

Combine like terms: 6.34428877 + 2.5 = 8.84428877
t = 8.84428877

Simplifying
t = 8.84428877


Subproblem 2
t + -2.5 = -6.34428877

Simplifying
t + -2.5 = -6.34428877

Reorder the terms:
-2.5 + t = -6.34428877

Solving
-2.5 + t = -6.34428877

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 = -6.34428877 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -6.34428877 + 2.5
t = -6.34428877 + 2.5

Combine like terms: -6.34428877 + 2.5 = -3.84428877
t = -3.84428877

Simplifying
t = -3.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.84428877, -3.84428877}

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