# How do you solve sqrt(9-b)=sqrt(1-9b)?

Jun 12, 2017

$b = - 1$

#### Explanation:

We have: $\sqrt{9 - b} = \sqrt{1 - 9 b}$

Let's square both sides of the equation:

$R i g h t a r r o w {\left(\sqrt{9 - b}\right)}^{2} = {\left(\sqrt{1 - 9 b}\right)}^{2}$

$R i g h t a r r o w 9 - b = 1 - 9 b$

Then, let's add $9 b$ to both sides:

$R i g h t a r r o w 9 - b + 9 b = 1 - 9 b + 9 b$

$R i g h t a r r o w 9 + 8 b = 1$

Now, let's subtract $9$ from both sides:

$R i g h t a r r o w 9 + 8 b - 8 = 1 - 9$

$R i g h t a r r o w 8 b = - 8$

Finally, to solve for $b$, let's divide both sides by $8$:

$R i g h t a r r o w \frac{8 b}{8} = - \frac{8}{8}$

$\therefore b = - 1$

Therefore, the solution to the equation is $b = - 1$.