Question

Use factoring to find the solutions for 30=−x2+13x
.(1 point)
Responses

x=−10,−3
x equals negative 10 comma negative 3

x=3,10
x equals 3 comma 10

x=−3,10
x equals negative 3 comma 10

x=−10,3

Answer 1

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

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

Multiply through by -1 to make the leading coefficient positive:

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

Next, we can factor the quadratic. We need two numbers that multiply to 30 and add up to -13. These numbers are -3 and -10.

So we can factor the equation as:

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

Setting each factor equal to zero gives us the solutions:

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

Thus, the solutions are

\[
x = 3, 10
\]

So the correct response is:

**x=3,10**