b^2-7b+8=0

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Solution for b^2-7b+8=0 equation: 


Simplifying
b2 + -7b + 8 = 0

Reorder the terms:
8 + -7b + b2 = 0

Solving
8 + -7b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7b + -8 + b2 = 0 + -8

Reorder the terms:
8 + -8 + -7b + b2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7b + b2 = 0 + -8
-7b + b2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7b + b2 = -8

The b term is -7b.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7b + 12.25 + b2 = -8 + 12.25

Reorder the terms:
12.25 + -7b + b2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7b + b2 = 4.25

Factor a perfect square on the left side:
(b + -3.5)(b + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(b + -3.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
b + -3.5 = 2.061552813

Simplifying
b + -3.5 = 2.061552813

Reorder the terms:
-3.5 + b = 2.061552813

Solving
-3.5 + b = 2.061552813

Solving for variable 'b'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + b = 2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + b = 2.061552813 + 3.5
b = 2.061552813 + 3.5

Combine like terms: 2.061552813 + 3.5 = 5.561552813
b = 5.561552813

Simplifying
b = 5.561552813


Subproblem 2
b + -3.5 = -2.061552813

Simplifying
b + -3.5 = -2.061552813

Reorder the terms:
-3.5 + b = -2.061552813

Solving
-3.5 + b = -2.061552813

Solving for variable 'b'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + b = -2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + b = -2.061552813 + 3.5
b = -2.061552813 + 3.5

Combine like terms: -2.061552813 + 3.5 = 1.438447187
b = 1.438447187

Simplifying
b = 1.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {5.561552813, 1.438447187}

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