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.

Answers:

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!

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