b^2-16b-66=0

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Solution for b^2-16b-66=0 equation:


Simplifying
b2 + -16b + -66 = 0

Reorder the terms:
-66 + -16b + b2 = 0

Solving
-66 + -16b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + -16b + 66 + b2 = 0 + 66

Reorder the terms:
-66 + 66 + -16b + b2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + -16b + b2 = 0 + 66
-16b + b2 = 0 + 66

Combine like terms: 0 + 66 = 66
-16b + b2 = 66

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 = 66 + 64

Reorder the terms:
64 + -16b + b2 = 66 + 64

Combine like terms: 66 + 64 = 130
64 + -16b + b2 = 130

Factor a perfect square on the left side:
(b + -8)(b + -8) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(b + -8) equal to 11.401754251 and -11.401754251.

Subproblem 1

b + -8 = 11.401754251 Simplifying b + -8 = 11.401754251 Reorder the terms: -8 + b = 11.401754251 Solving -8 + b = 11.401754251 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 = 11.401754251 + 8 Combine like terms: -8 + 8 = 0 0 + b = 11.401754251 + 8 b = 11.401754251 + 8 Combine like terms: 11.401754251 + 8 = 19.401754251 b = 19.401754251 Simplifying b = 19.401754251

Subproblem 2

b + -8 = -11.401754251 Simplifying b + -8 = -11.401754251 Reorder the terms: -8 + b = -11.401754251 Solving -8 + b = -11.401754251 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 = -11.401754251 + 8 Combine like terms: -8 + 8 = 0 0 + b = -11.401754251 + 8 b = -11.401754251 + 8 Combine like terms: -11.401754251 + 8 = -3.401754251 b = -3.401754251 Simplifying b = -3.401754251

Solution

The solution to the problem is based on the solutions from the subproblems. b = {19.401754251, -3.401754251}

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