t^2-6t=35

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Solution for t^2-6t=35 equation: 


Simplifying
t2 + -6t = 35

Reorder the terms:
-6t + t2 = 35

Solving
-6t + t2 = 35

Solving for variable 't'.

Reorder the terms:
-35 + -6t + t2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -6t + 35 + t2 = 0 + 35

Reorder the terms:
-35 + 35 + -6t + t2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -6t + t2 = 0 + 35
-6t + t2 = 0 + 35

Combine like terms: 0 + 35 = 35
-6t + t2 = 35

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 35 + 9

Reorder the terms:
9 + -6t + t2 = 35 + 9

Combine like terms: 35 + 9 = 44
9 + -6t + t2 = 44

Factor a perfect square on the left side:
(t + -3)(t + -3) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(t + -3) equal to 6.633249581 and -6.633249581.


Subproblem 1
t + -3 = 6.633249581

Simplifying
t + -3 = 6.633249581

Reorder the terms:
-3 + t = 6.633249581

Solving
-3 + t = 6.633249581

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 6.633249581 + 3

Combine like terms: -3 + 3 = 0
0 + t = 6.633249581 + 3
t = 6.633249581 + 3

Combine like terms: 6.633249581 + 3 = 9.633249581
t = 9.633249581

Simplifying
t = 9.633249581


Subproblem 2
t + -3 = -6.633249581

Simplifying
t + -3 = -6.633249581

Reorder the terms:
-3 + t = -6.633249581

Solving
-3 + t = -6.633249581

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -6.633249581 + 3

Combine like terms: -3 + 3 = 0
0 + t = -6.633249581 + 3
t = -6.633249581 + 3

Combine like terms: -6.633249581 + 3 = -3.633249581
t = -3.633249581

Simplifying
t = -3.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.633249581, -3.633249581}

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