# Worksheet: Completing the Square

**Instructions:** Solve each quadratic equation by completing the square. Show all your work, and write the solutions in both simplified radical form and as decimal approximations.

**1.** Solve the equation: $$x^2 – 6x + 9 = 0$$

**2.** Solve the equation: $$2x^2 + 12x + 18 = 0$$

**3.** Solve the equation: $$3x^2 – 10x + 7 = 0$$

**4.** Solve the equation: $$x^2 + 4x – 5 = 0$$

**5.** Solve the equation: $$4x^2 – 20x + 25 = 0$$

**6.** Solve the equation: $$2x^2 – 8x – 6 = 0$$

**7.** Solve the equation: $$x^2 + 10x + 25 = 0$$

**8.** Solve the equation: $$3x^2 – 21x + 36 = 0$$

**9.** Solve the equation: $$5x^2 + 2x – 3 = 0$$

**10.** Solve the equation: $$6x^2 – 9x – 15 = 0$$

Remember: When completing the square, follow these steps:

1. Move the constant term to the other side of the equation.
2. Make sure the coefficient of $$x^2$$ is 1 (divide the equation by the coefficient if necessary).
3. Add and subtract $$\left(\frac{\text{coefficient of } x}{2}\right)^2$$ inside the square of the binomial on the left side of the equation.
4. Factor the perfect square trinomial.
5. Solve for $$x$$ by taking the square root of both sides and simplifying.

1. $$x = 3$$
2. $$x = -3$$
3. $$x = \frac{5}{3}$$ or $$x = 1$$
4. $$x = 1$$ or $$x = -5$$
5. $$x = 2.5$$
6. $$x = 2$$ or $$x = -1$$
7. $$x = -5$$
8. $$x = 3$$ or $$x = 4$$
9. $$x = \frac{-1 \pm \sqrt{29}}{5}$$
10. $$x = -1$$ or $$x = \frac{5}{2}$$

Remember to check your solutions by substituting them back into the original equations!