b^2-18b+59=0

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Solution for b^2-18b+59=0 equation:


Simplifying
b2 + -18b + 59 = 0

Reorder the terms:
59 + -18b + b2 = 0

Solving
59 + -18b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-59' to each side of the equation.
59 + -18b + -59 + b2 = 0 + -59

Reorder the terms:
59 + -59 + -18b + b2 = 0 + -59

Combine like terms: 59 + -59 = 0
0 + -18b + b2 = 0 + -59
-18b + b2 = 0 + -59

Combine like terms: 0 + -59 = -59
-18b + b2 = -59

The b term is -18b.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18b + 81 + b2 = -59 + 81

Reorder the terms:
81 + -18b + b2 = -59 + 81

Combine like terms: -59 + 81 = 22
81 + -18b + b2 = 22

Factor a perfect square on the left side:
(b + -9)(b + -9) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(b + -9) equal to 4.69041576 and -4.69041576.

Subproblem 1

b + -9 = 4.69041576 Simplifying b + -9 = 4.69041576 Reorder the terms: -9 + b = 4.69041576 Solving -9 + b = 4.69041576 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + b = 4.69041576 + 9 Combine like terms: -9 + 9 = 0 0 + b = 4.69041576 + 9 b = 4.69041576 + 9 Combine like terms: 4.69041576 + 9 = 13.69041576 b = 13.69041576 Simplifying b = 13.69041576

Subproblem 2

b + -9 = -4.69041576 Simplifying b + -9 = -4.69041576 Reorder the terms: -9 + b = -4.69041576 Solving -9 + b = -4.69041576 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + b = -4.69041576 + 9 Combine like terms: -9 + 9 = 0 0 + b = -4.69041576 + 9 b = -4.69041576 + 9 Combine like terms: -4.69041576 + 9 = 4.30958424 b = 4.30958424 Simplifying b = 4.30958424

Solution

The solution to the problem is based on the solutions from the subproblems. b = {13.69041576, 4.30958424}

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