Final answer:
The quadratic equation -3x^2 = -3x - 18 does not have real solutions because the discriminant in the quadratic formula is negative, which means the equation yields no real values of x.
Step-by-step explanation:
The equation given by the student, -3x2 = -3x - 18, is a quadratic equation. To find the value of x that satisfies the equation, we first need to set it to zero by moving all the terms to one side of the equation. We get:
3x2 - 3x + 18 = 0.
This equation is not factorable using simple methods, so we have to use the quadratic formula, which is:
x = (-b ± √(b2 - 4ac)) / (2a).
Substituting the coefficients from our equation gives us:
x = (3 ± √((3)2 - 4(3)(18))) / (2(3)).
However, since the discriminant (b2 - 4ac) is negative, there are no real solutions for this equation, as the square root of a negative number does not yield a real number.