t^2-2t+1=37

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Solution for t^2-2t+1=37 equation: 


Simplifying
t2 + -2t + 1 = 37

Reorder the terms:
1 + -2t + t2 = 37

Solving
1 + -2t + t2 = 37

Solving for variable 't'.

Reorder the terms:
1 + -37 + -2t + t2 = 37 + -37

Combine like terms: 1 + -37 = -36
-36 + -2t + t2 = 37 + -37

Combine like terms: 37 + -37 = 0
-36 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -2t + 36 + t2 = 0 + 36

Reorder the terms:
-36 + 36 + -2t + t2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -2t + t2 = 0 + 36
-2t + t2 = 0 + 36

Combine like terms: 0 + 36 = 36
-2t + t2 = 36

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 36 + 1

Reorder the terms:
1 + -2t + t2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + -2t + t2 = 37

Factor a perfect square on the left side:
(t + -1)(t + -1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(t + -1) equal to 6.08276253 and -6.08276253.


Subproblem 1
t + -1 = 6.08276253

Simplifying
t + -1 = 6.08276253

Reorder the terms:
-1 + t = 6.08276253

Solving
-1 + t = 6.08276253

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 6.08276253 + 1

Combine like terms: -1 + 1 = 0
0 + t = 6.08276253 + 1
t = 6.08276253 + 1

Combine like terms: 6.08276253 + 1 = 7.08276253
t = 7.08276253

Simplifying
t = 7.08276253


Subproblem 2
t + -1 = -6.08276253

Simplifying
t + -1 = -6.08276253

Reorder the terms:
-1 + t = -6.08276253

Solving
-1 + t = -6.08276253

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -6.08276253 + 1

Combine like terms: -1 + 1 = 0
0 + t = -6.08276253 + 1
t = -6.08276253 + 1

Combine like terms: -6.08276253 + 1 = -5.08276253
t = -5.08276253

Simplifying
t = -5.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.08276253, -5.08276253}

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