1. You asked for more questions to prepare for the TOLC test.
2. Since you did not specify a particular topic, here is a sample algebra question to practice:
**Problem:** Solve for $x$ in the equation $$2x^2 - 5x + 3 = 0$$.
3. The formula to solve quadratic equations is the quadratic formula:
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
where $a$, $b$, and $c$ are coefficients from the quadratic equation $ax^2 + bx + c = 0$.
4. For our equation, $a=2$, $b=-5$, and $c=3$.
5. Calculate the discriminant:
$$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 2 \times 3 = 25 - 24 = 1$$
6. Since $\Delta > 0$, there are two real solutions.
7. Substitute into the quadratic formula:
$$x = \frac{-(-5) \pm \sqrt{1}}{2 \times 2} = \frac{5 \pm 1}{4}$$
8. Calculate each solution:
- $$x_1 = \frac{5 + 1}{4} = \frac{6}{4} = 1.5$$
- $$x_2 = \frac{5 - 1}{4} = \frac{4}{4} = 1$$
9. Therefore, the solutions are $$x = 1.5$$ and $$x = 1$$.
This is a typical algebra problem you might encounter on the TOLC test. Practice similar problems to improve your skills.
Quadratic Equation F64146
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.