Question

Use factoring to find the solutions for 30=−x^2+13x
. (1 point)
Responses

x=−10, −3
x=−10, −3

x=−3, 10
x=−3, 10

x=−10, 3
x=−10, 3

x=3, 10

Answer 1

To solve the equation \( 30 = -x^2 + 13x \), we first rearrange it into standard form:

\[
-x^2 + 13x - 30 = 0
\]

Next, we can multiply the entire equation by -1 to make factoring easier:

\[
x^2 - 13x + 30 = 0
\]

Now, we will factor the quadratic equation. We need to find two numbers that multiply to \( 30 \) (the constant term) and add to \( -13 \) (the coefficient of \( x \)). The numbers that satisfy this are \( -3 \) and \( -10 \).

Thus, we can write the factored form as:

\[
(x - 3)(x - 10) = 0
\]

Setting each factor equal to zero gives us the solutions:

1. \( x - 3 = 0 \) → \( x = 3 \)
2. \( x - 10 = 0 \) → \( x = 10 \)

Therefore, the solutions are:

\[
x = 3, 10
\]

The correct response from the options provided is:

**x=3, 10**