b^2-10b+2=0

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


Simplifying
b2 + -10b + 2 = 0

Reorder the terms:
2 + -10b + b2 = 0

Solving
2 + -10b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -10b + -2 + b2 = 0 + -2

Reorder the terms:
2 + -2 + -10b + b2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -10b + b2 = 0 + -2
-10b + b2 = 0 + -2

Combine like terms: 0 + -2 = -2
-10b + b2 = -2

The b term is -10b.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10b + 25 + b2 = -2 + 25

Reorder the terms:
25 + -10b + b2 = -2 + 25

Combine like terms: -2 + 25 = 23
25 + -10b + b2 = 23

Factor a perfect square on the left side:
(b + -5)(b + -5) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(b + -5) equal to 4.795831523 and -4.795831523.

Subproblem 1

b + -5 = 4.795831523 Simplifying b + -5 = 4.795831523 Reorder the terms: -5 + b = 4.795831523 Solving -5 + b = 4.795831523 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = 4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + b = 4.795831523 + 5 b = 4.795831523 + 5 Combine like terms: 4.795831523 + 5 = 9.795831523 b = 9.795831523 Simplifying b = 9.795831523

Subproblem 2

b + -5 = -4.795831523 Simplifying b + -5 = -4.795831523 Reorder the terms: -5 + b = -4.795831523 Solving -5 + b = -4.795831523 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = -4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + b = -4.795831523 + 5 b = -4.795831523 + 5 Combine like terms: -4.795831523 + 5 = 0.204168477 b = 0.204168477 Simplifying b = 0.204168477

Solution

The solution to the problem is based on the solutions from the subproblems. b = {9.795831523, 0.204168477}

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