Use factoring to find the solutions for 30=−x2+13x

Question

.(1 point)
Responses

x=−10,3
x equals negative 10 comma 3

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

x=3,10
x equals 3 comma 10

x=−3,10

Answer 1

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

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

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

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

Next, we look for two numbers that multiply to \( 30 \) and add to \( -13 \). The two numbers that satisfy these conditions are \( -3 \) and \( -10 \).

Now, we can factor the quadratic equation:

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

Setting each factor equal to zero gives us the solutions:

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

\[ x - 10 = 0 \quad \Rightarrow \quad x = 10 \]

Thus, the solutions are:

\[ x = 3, 10 \]

So the correct response is:

x=3,10