Practice: The Quadratic Formula

The Formula: For any equation $ax^2 + bx + c = 0$, use: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Top Tip: Always identify your coefficients first. For example, in $x^2 - 3x - 5 = 0$, $a=1, b=-3, c=-5$.

1. $x^2 + 5x + 4 = 0$

2. $x^2 - 7x + 10 = 0$

3. $x^2 + 2x - 8 = 0$

4. $x^2 - 4x - 12 = 0$

5. $2x^2 + 5x + 2 = 0$

6. $3x^2 - 10x + 3 = 0$

7. $x^2 + 6x + 9 = 0$

8. $2x^2 - 3x - 5 = 0$

9. $5x^2 + 13x - 6 = 0$

10. $x^2 + 10x + 15 = 0$

Rearrangement Required

11. $x^2 + 8x = -12$

12. $x^2 = 3x + 10$

13. $2x^2 + 7x = 4$

14. $x^2 - 10 = 3x$

15. $3x^2 = 2x + 5$

16. $x(x + 5) = 14$

17. $x^2 + 4x = 1$

18. $6x^2 - 7 = 11x$

19. $2x(x - 3) = 8$

20. $4x^2 + 1 = 4x$

💡 Need a Hint?

Before you use the formula, you must have the equation equal to zero.

Questions 11-15: Move the terms by doing the opposite. For #11, add 12 to both sides to get $x^2 + 8x + 12 = 0$.
Questions 16 & 19: Expand the brackets first! Multiply the term outside by everything inside, then move the constant to the left.
Signs Matter: If you have $x^2 - 4x$, your $b$ value is -4. When you put this into $-b$, it becomes $-(-4)$ which is +4.
No $x$ term? If an equation was $x^2 - 9 = 0$, then $b=0$.