Subjects algebra

Quadratic Equation F64146

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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.