Question

Which value of x is the solution to this equation?
5x ^ 2 = 30x - 45
O x = 3
x = 5
x=4 & x=9

Answer 1

To solve the equation \( 5x^2 = 30x - 45 \), we first rearrange the equation to set it to zero:

\[
5x^2 - 30x + 45 = 0
\]

Next, we can simplify the equation by dividing all terms by 5:

\[
x^2 - 6x + 9 = 0
\]

Now, we can factor the quadratic equation:

\[
(x - 3)(x - 3) = 0
\]

This gives us:

\[
(x - 3)^2 = 0
\]

Therefore, the solution is:

\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]

So the solution to the equation \( 5x^2 = 30x - 45 \) is \( x = 3 \).

Among the options provided:
- O \( x = 3 \) (This is correct)
- \( x = 5 \) (Incorrect)
- \( x = 4 \) & \( x = 9 \) (Incorrect)

Thus, the answer is:

\[
\boxed{3}
\]