b^2-16b-8=0

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Solution for b^2-16b-8=0 equation:


Simplifying
b2 + -16b + -8 = 0

Reorder the terms:
-8 + -16b + b2 = 0

Solving
-8 + -16b + 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 + -16b + 8 + b2 = 0 + 8

Reorder the terms:
-8 + 8 + -16b + b2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -16b + b2 = 0 + 8
-16b + b2 = 0 + 8

Combine like terms: 0 + 8 = 8
-16b + b2 = 8

The b term is -16b.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16b + 64 + b2 = 8 + 64

Reorder the terms:
64 + -16b + b2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + -16b + b2 = 72

Factor a perfect square on the left side:
(b + -8)(b + -8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(b + -8) equal to 8.485281374 and -8.485281374.

Subproblem 1

b + -8 = 8.485281374 Simplifying b + -8 = 8.485281374 Reorder the terms: -8 + b = 8.485281374 Solving -8 + b = 8.485281374 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = 8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + b = 8.485281374 + 8 b = 8.485281374 + 8 Combine like terms: 8.485281374 + 8 = 16.485281374 b = 16.485281374 Simplifying b = 16.485281374

Subproblem 2

b + -8 = -8.485281374 Simplifying b + -8 = -8.485281374 Reorder the terms: -8 + b = -8.485281374 Solving -8 + b = -8.485281374 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = -8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + b = -8.485281374 + 8 b = -8.485281374 + 8 Combine like terms: -8.485281374 + 8 = -0.485281374 b = -0.485281374 Simplifying b = -0.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. b = {16.485281374, -0.485281374}

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