Question

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 negative 3 comma 10

x=3,10
x equals 3 comma 10

x=−10,3
x equals negative 10 comma 3
Remaining Attempts : 3
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Answer 1

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

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

Next, we multiply through by -1 to make the leading coefficient positive:

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

Now we can factor the quadratic expression. 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 these conditions are \( -3 \) and \( -10 \).

Thus, we can factor the equation as follows:

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

Now, we set each factor equal to zero and solve for \( x \):

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

Thus, the solutions are \( x = 3 \) and \( x = 10 \).

Based on the given options, the correct response is:

x = 3, 10