Question
Use factoring to find the solutions for 30=−x2+13x .(1 point)
Responses
x=3,10
x equals 3 comma 10
x=−10,−3
x equals negative 10 comma negative 3
x=−10,3
x equals negative 10 comma 3
x=−3,10
Responses
x=3,10
x equals 3 comma 10
x=−10,−3
x equals negative 10 comma negative 3
x=−10,3
x equals negative 10 comma 3
x=−3,10
Answers
GPT-4o mini
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 gives:
\[
x^2 - 13x + 30 = 0
\]
Next, we will factor the quadratic equation. We are looking for two numbers that multiply to 30 (the constant term) and add up to -13 (the coefficient of \( x \)). The pair of numbers that satisfies these conditions is -3 and -10.
Thus, we can factor the equation as follows:
\[
(x - 3)(x - 10) = 0
\]
Setting each factor equal to zero gives us the solutions:
\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]
\[
x - 10 = 0 \quad \Rightarrow \quad x = 10
\]
So the solutions are:
\[
x = 3, 10
\]
The correct response is:
**x=3,10** or **x equals 3 comma 10**.
\[
-x^2 + 13x - 30 = 0
\]
Multiplying through by -1 gives:
\[
x^2 - 13x + 30 = 0
\]
Next, we will factor the quadratic equation. We are looking for two numbers that multiply to 30 (the constant term) and add up to -13 (the coefficient of \( x \)). The pair of numbers that satisfies these conditions is -3 and -10.
Thus, we can factor the equation as follows:
\[
(x - 3)(x - 10) = 0
\]
Setting each factor equal to zero gives us the solutions:
\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]
\[
x - 10 = 0 \quad \Rightarrow \quad x = 10
\]
So the solutions are:
\[
x = 3, 10
\]
The correct response is:
**x=3,10** or **x equals 3 comma 10**.