Solve. $$ (y+2)^{2}-10(y+2)=-9 $$ If there is more than one solution, separate them with commas.

Question

UpStudy AI · Accepted Answer

Let $$ u = y+2 $$. Then the equation becomes

$$
u^2 - 10u = -9.
$$

Add 9 to both sides to obtain

$$
u^2 - 10u + 9 = 0.
$$

Factor the quadratic:

$$
(u-1)(u-9) = 0.
$$

So, we have

$$
u = 1 \quad \text{or} \quad u = 9.
$$

Recall that $$ u = y+2 $$. Therefore, if $$ u = 1 $$:

$$
y+2 = 1 \implies y = -1,
$$

and if $$ u = 9 $$:

$$
y+2 = 9 \implies y = 7.
$$

The solutions are $$ y = -1 $$ and $$ y = 7 $$.
The solutions are $$ y = -1 $$ and $$ y = 7 $$.

Solve.

If there is more than one solution, separate them with commas.