b^2-8b+10=0

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Solution for b^2-8b+10=0 equation: 


Simplifying
b2 + -8b + 10 = 0

Reorder the terms:
10 + -8b + b2 = 0

Solving
10 + -8b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8b + -10 + b2 = 0 + -10

Reorder the terms:
10 + -10 + -8b + b2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8b + b2 = 0 + -10
-8b + b2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8b + b2 = -10

The b term is -8b.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8b + 16 + b2 = -10 + 16

Reorder the terms:
16 + -8b + b2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + -8b + b2 = 6

Factor a perfect square on the left side:
(b + -4)(b + -4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(b + -4) equal to 2.449489743 and -2.449489743.


Subproblem 1
b + -4 = 2.449489743

Simplifying
b + -4 = 2.449489743

Reorder the terms:
-4 + b = 2.449489743

Solving
-4 + b = 2.449489743

Solving for variable 'b'.

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

Add '4' to each side of the equation.
-4 + 4 + b = 2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + b = 2.449489743 + 4
b = 2.449489743 + 4

Combine like terms: 2.449489743 + 4 = 6.449489743
b = 6.449489743

Simplifying
b = 6.449489743


Subproblem 2
b + -4 = -2.449489743

Simplifying
b + -4 = -2.449489743

Reorder the terms:
-4 + b = -2.449489743

Solving
-4 + b = -2.449489743

Solving for variable 'b'.

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

Add '4' to each side of the equation.
-4 + 4 + b = -2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + b = -2.449489743 + 4
b = -2.449489743 + 4

Combine like terms: -2.449489743 + 4 = 1.550510257
b = 1.550510257

Simplifying
b = 1.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {6.449489743, 1.550510257}

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