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=−10,3 x equals negative 10 comma 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 through by -1 to make the leading coefficient positive:

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

Now we need to factor the quadratic expression \( x^2 - 13x + 30 \). We look for two numbers that multiply to 30 (the constant term) and add up to -13 (the coefficient of \( x \)). The numbers -3 and -10 fit this requirement:

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

Now, we can find the solutions by setting each factor equal to zero:

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

Thus, the solutions to the equation are:

\[ x = 3, , 10 \]

The correct answer from the options given is:

x=3,10 or x equals 3 comma 10.