Question

Which of the following are solutions to the equation below?

Check all that apply.

x2 + 3x - 18 = 0

A. 9
B. 3
C. -3
D. 6
E. 18
F. -6

Answer 1

B.3 and F.-6
Those are the two solutions


Hope I didn't mess up for your sake!

Answer 2

The solutions are -6 and 3.

Options B and F.

Explanation:

To find the solution of this quadratic equation, we could apply several simple steps.

First, we write to factor, which one is gonna have a variable followed by a sign. The first factor is gonna have the same sign as the second term of the quadratic expression, which is positive. The second factor is gonna have a negative sign, which is given by multiplying the sign of the second term and the third term. So, the factors are gonna stay like this:

`x^(2) +3x-18=(x+a)(x-b)`

Now, we have to find two numbers (a and b), which product result 18, and subtract result in 3. Those numbers are 6 and 3, because 6(3) = 18, and 6-3=3. The numbers need to be subtracted, because the factor have different signs.

Therefore, the solution factors are:

`x^(2) +3x-18=(x+6)(x-3)`

At last, we say that each factor is equal to zero to find the exact solutions:

`x_(1) +6=0\\x_(1) =-6\\x_(2)-3=0\\x_(2)=3`

Hence, the solutions are -6 and 3. Options B and F.