Question

Solve the equation by factoring:
9b^2+21b+1=-9

Answer 1

`9b^2+21b+1=-9 \\ 9b^2+21b+1+9=0 \\ 9b^2+21b+10=0 \\ 9b^2+15b+6b+10=0 \\ 3b(3b+5)+2(3b+5)=0 \\ (3b+2)(3b+5)=0 \\ \\ 3b+2=0 \ \ \ \ or \ \ \ \ 3b+5=0 \\3b=-2 \ \ \ \ \ \ \ or \ \ \ \ 3b=-5 \\ b=- (2)/(3) \ \ \ \ \ \ \ \ or \ \ \ \ b=- (5)/(3)=-1 (2)/(3) \\ \\ Answer: \ \ b=- (2)/(3); \ \ b=-1 (2)/(3)`

Answer 2

Hello!

Simplifying:
9b2 + 21b + 1 = -9

Reorder the terms:
1 + 21b + 9b2 = -9

Solving:
1 + 21b + 9b2 = -9

Solving for variable 'b'.

Reorder the terms:
1 + 9 + 21b + 9b2 = -9 + 9

Combine like terms:
1 + 9 = 10 10 + 21b + 9b2 = -9 + 9

Combine like terms:
-9 + 9 = 0 10 + 21b + 9b2 = 0

Factor a trinomial.
(5 + 3b)(2 + 3b) = 0

Subproblem 1: Set the factor '(5 + 3b)' equal to zero and attempt to solve:

Simplifying:
5 + 3b = 0

Solving:
5 + 3b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 3b = 0 + -5

Combine like terms:
5 + -5 = 0 0 + 3b = 0 + -5
3b = 0 + -5

Combine like terms: 0 + -5 = -5
3b = -5
Divide each side by '3'.
b = -1.666666667

Subproblem 2: Set the factor '(2 + 3b)' equal to zero and attempt to solve:

Simplifying:
2 + 3b = 0

Solving:
2 + 3b = 0

Move all terms containing b to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + 3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3b = 0 + -2
3b = 0 + -2

Combine like terms: 0 + -2 = -2
3b = -2

Divide each side by '3'.
b = -0.6666666667

Simplifying:
b = -0.6666666667

Solution:

b = {-1.666666667, -0.6666666667}


Hope this Helps! Took Me A LOT of time lol! Have A Wonderful Day! :)