Solve the following equation using the quadratic formula.
\[
(x-8)(x-2)=-9
\]
The solution set is (Simplify your answer.)

Answer

Expert–verified

Hide Steps

Answer

The only solution for $x$ is $\boxed{5}$.

Steps

Step 1 ：Expanding the product on the left, we have $(x-8)(x-2) = -9$, so $x^2 - 10x + 16 = -9$.

Step 2 ：So, $x^2 - 10x + 16 + 9 = 0$. Simplifying the left side gives $x^2 - 10x + 25 = 0$.

Step 3 ：This can be factored as $(x - 5)(x - 5) = 0$.

Step 4 ：The only solution for $x$ is $\boxed{5}$.