b^2-34b-289=0

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Solution for b^2-34b-289=0 equation: 


Simplifying
b2 + -34b + -289 = 0

Reorder the terms:
-289 + -34b + b2 = 0

Solving
-289 + -34b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '289' to each side of the equation.
-289 + -34b + 289 + b2 = 0 + 289

Reorder the terms:
-289 + 289 + -34b + b2 = 0 + 289

Combine like terms: -289 + 289 = 0
0 + -34b + b2 = 0 + 289
-34b + b2 = 0 + 289

Combine like terms: 0 + 289 = 289
-34b + b2 = 289

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 = 289 + 289

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

Combine like terms: 289 + 289 = 578
289 + -34b + b2 = 578

Factor a perfect square on the left side:
(b + -17)(b + -17) = 578

Calculate the square root of the right side: 24.04163056

Break this problem into two subproblems by setting 
(b + -17) equal to 24.04163056 and -24.04163056.


Subproblem 1
b + -17 = 24.04163056

Simplifying
b + -17 = 24.04163056

Reorder the terms:
-17 + b = 24.04163056

Solving
-17 + b = 24.04163056

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 = 24.04163056 + 17

Combine like terms: -17 + 17 = 0
0 + b = 24.04163056 + 17
b = 24.04163056 + 17

Combine like terms: 24.04163056 + 17 = 41.04163056
b = 41.04163056

Simplifying
b = 41.04163056


Subproblem 2
b + -17 = -24.04163056

Simplifying
b + -17 = -24.04163056

Reorder the terms:
-17 + b = -24.04163056

Solving
-17 + b = -24.04163056

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 = -24.04163056 + 17

Combine like terms: -17 + 17 = 0
0 + b = -24.04163056 + 17
b = -24.04163056 + 17

Combine like terms: -24.04163056 + 17 = -7.04163056
b = -7.04163056

Simplifying
b = -7.04163056


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {41.04163056, -7.04163056}

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