Question

23 Which value of x is a solution to this equation?
Q
3x ^ 2 - 30x - 72 = 0
B x = - 4
D x = - 6
C x = - 2
A x = - 12

Answer 1

To solve the equation \(3x^2 - 30x - 72 = 0\), we can either factor the equation or use the quadratic formula. In this case, let's try factoring.

First, we can simplify the equation by dividing all terms by 3:

\[
x^2 - 10x - 24 = 0
\]

Next, we look for two numbers that multiply to \(-24\) (the constant term) and add to \(-10\) (the coefficient of the linear term). The numbers \(-12\) and \(2\) work because:

\[
-12 \times 2 = -24
\]
\[
-12 + 2 = -10
\]

We can factor the quadratic as follows:

\[
(x - 12)(x + 2) = 0
\]

Setting each factor equal to zero gives us the solutions:

\[
x - 12 = 0 \quad \Rightarrow \quad x = 12
\]
\[
x + 2 = 0 \quad \Rightarrow \quad x = -2
\]

Now, looking at the options provided:
- A) \(x = -12\)
- B) \(x = -4\)
- C) \(x = -2\) (which is a solution)
- D) \(x = -6\)

The value of \(x\) that is a solution to the equation is:

\[
\boxed{-2}
\]