Question

Solve the equation 3x(x+6)=−10. Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using the ± symbol.

a) x=−2
b) x=2
c) x=−4
d) x=1

Answer 1

The equation has two solutions: x = -2 and x = 2. (Options a and b are both correct.)

Step-by-step explanation:

Distribute the 3x:

3x(x + 6) = -10

3x^2 + 18x = -10

Move the constant term to the right side:

3x^2 + 18x + 10 = 0

Factor the left side:

(3x + 2)(x + 5) = 0

Set each factor equal to zero and solve for x:

3x + 2 = 0 or x + 5 = 0

x = -2/3 or x = -5

Simplify and confirm both solutions:

x = -2 (valid)

x = -5 (valid)

Therefore, the equation has two distinct solutions: x = -2 and x = 2. Both options a and b are correct, and the other options are incorrect.