b^2-34b+289=45

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Solution for b^2-34b+289=45 equation: 


Simplifying
b2 + -34b + 289 = 45

Reorder the terms:
289 + -34b + b2 = 45

Solving
289 + -34b + b2 = 45

Solving for variable 'b'.

Reorder the terms:
289 + -45 + -34b + b2 = 45 + -45

Combine like terms: 289 + -45 = 244
244 + -34b + b2 = 45 + -45

Combine like terms: 45 + -45 = 0
244 + -34b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-244' to each side of the equation.
244 + -34b + -244 + b2 = 0 + -244

Reorder the terms:
244 + -244 + -34b + b2 = 0 + -244

Combine like terms: 244 + -244 = 0
0 + -34b + b2 = 0 + -244
-34b + b2 = 0 + -244

Combine like terms: 0 + -244 = -244
-34b + b2 = -244

The b term is -34b.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34b + 289 + b2 = -244 + 289

Reorder the terms:
289 + -34b + b2 = -244 + 289

Combine like terms: -244 + 289 = 45
289 + -34b + b2 = 45

Factor a perfect square on the left side:
(b + -17)(b + -17) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(b + -17) equal to 6.708203933 and -6.708203933.


Subproblem 1
b + -17 = 6.708203933

Simplifying
b + -17 = 6.708203933

Reorder the terms:
-17 + b = 6.708203933

Solving
-17 + b = 6.708203933

Solving for variable 'b'.

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

Add '17' to each side of the equation.
-17 + 17 + b = 6.708203933 + 17

Combine like terms: -17 + 17 = 0
0 + b = 6.708203933 + 17
b = 6.708203933 + 17

Combine like terms: 6.708203933 + 17 = 23.708203933
b = 23.708203933

Simplifying
b = 23.708203933


Subproblem 2
b + -17 = -6.708203933

Simplifying
b + -17 = -6.708203933

Reorder the terms:
-17 + b = -6.708203933

Solving
-17 + b = -6.708203933

Solving for variable 'b'.

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

Add '17' to each side of the equation.
-17 + 17 + b = -6.708203933 + 17

Combine like terms: -17 + 17 = 0
0 + b = -6.708203933 + 17
b = -6.708203933 + 17

Combine like terms: -6.708203933 + 17 = 10.291796067
b = 10.291796067

Simplifying
b = 10.291796067


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {23.708203933, 10.291796067}

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