b^2+18b+43=0

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Solution for b^2+18b+43=0 equation:


Simplifying
b2 + 18b + 43 = 0

Reorder the terms:
43 + 18b + b2 = 0

Solving
43 + 18b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + 18b + -43 + b2 = 0 + -43

Reorder the terms:
43 + -43 + 18b + b2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 18b + b2 = 0 + -43
18b + b2 = 0 + -43

Combine like terms: 0 + -43 = -43
18b + b2 = -43

The b term is 18b.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18b + 81 + b2 = -43 + 81

Reorder the terms:
81 + 18b + b2 = -43 + 81

Combine like terms: -43 + 81 = 38
81 + 18b + b2 = 38

Factor a perfect square on the left side:
(b + 9)(b + 9) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(b + 9) equal to 6.164414003 and -6.164414003.

Subproblem 1

b + 9 = 6.164414003 Simplifying b + 9 = 6.164414003 Reorder the terms: 9 + b = 6.164414003 Solving 9 + b = 6.164414003 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = 6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + b = 6.164414003 + -9 b = 6.164414003 + -9 Combine like terms: 6.164414003 + -9 = -2.835585997 b = -2.835585997 Simplifying b = -2.835585997

Subproblem 2

b + 9 = -6.164414003 Simplifying b + 9 = -6.164414003 Reorder the terms: 9 + b = -6.164414003 Solving 9 + b = -6.164414003 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = -6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + b = -6.164414003 + -9 b = -6.164414003 + -9 Combine like terms: -6.164414003 + -9 = -15.164414003 b = -15.164414003 Simplifying b = -15.164414003

Solution

The solution to the problem is based on the solutions from the subproblems. b = {-2.835585997, -15.164414003}

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