b^2+12b-32=0

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Solution for b^2+12b-32=0 equation:


Simplifying
b2 + 12b + -32 = 0

Reorder the terms:
-32 + 12b + b2 = 0

Solving
-32 + 12b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 12b + 32 + b2 = 0 + 32

Reorder the terms:
-32 + 32 + 12b + b2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 12b + b2 = 0 + 32
12b + b2 = 0 + 32

Combine like terms: 0 + 32 = 32
12b + b2 = 32

The b term is 12b.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12b + 36 + b2 = 32 + 36

Reorder the terms:
36 + 12b + b2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + 12b + b2 = 68

Factor a perfect square on the left side:
(b + 6)(b + 6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(b + 6) equal to 8.246211251 and -8.246211251.

Subproblem 1

b + 6 = 8.246211251 Simplifying b + 6 = 8.246211251 Reorder the terms: 6 + b = 8.246211251 Solving 6 + b = 8.246211251 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + b = 8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + b = 8.246211251 + -6 b = 8.246211251 + -6 Combine like terms: 8.246211251 + -6 = 2.246211251 b = 2.246211251 Simplifying b = 2.246211251

Subproblem 2

b + 6 = -8.246211251 Simplifying b + 6 = -8.246211251 Reorder the terms: 6 + b = -8.246211251 Solving 6 + b = -8.246211251 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + b = -8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + b = -8.246211251 + -6 b = -8.246211251 + -6 Combine like terms: -8.246211251 + -6 = -14.246211251 b = -14.246211251 Simplifying b = -14.246211251

Solution

The solution to the problem is based on the solutions from the subproblems. b = {2.246211251, -14.246211251}

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