Algebra Practice Test

To determine the solutions for the expression \( x^2 + x - 30 \), we can start by using the quadratic formula or attempting to factor the quadratic equation. The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \), where in this case, \( a = 1 \), \( b = 1 \), and \( c = -30 \).

Next, we can calculate the discriminant, which is given by \( D = b^2 - 4ac \). Substituting the values we have:

\[

D = 1^2 - 4 \cdot 1 \cdot (-30) = 1 + 120 = 121

\]

Since the discriminant is a positive number, this indicates that there are two real and distinct solutions for the quadratic equation. In the context of this question, the expression \( x^2 + x - 30 \) can be factored as \( (x - 5)(x + 6) = 0 \), which gives the solutions \( x = 5 \) and \( x = -6 \).

Therefore, the correct response is that there are indeed two real solutions. The reasoning