# Completing the Square Worksheet Pdf

__Worksheet: Completing the Square__

__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:

- Move the constant term to the other side of the equation.
- Make sure the coefficient of \(x^2\) is 1 (divide the equation by the coefficient if necessary).
- 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.
- Factor the perfect square trinomial.
- Solve for \(x\) by taking the square root of both sides and simplifying.

### Answers:

- \(x = 3\)
- \(x = -3\)
- \(x = \frac{5}{3}\) or \(x = 1\)
- \(x = 1\) or \(x = -5\)
- \(x = 2.5\)
- \(x = 2\) or \(x = -1\)
- \(x = -5\)
- \(x = 3\) or \(x = 4\)
- \(x = \frac{-1 \pm \sqrt{29}}{5}\)
- \(x = -1\) or \(x = \frac{5}{2}\)

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

Download here for Pdf Version Completing the Square Pdf

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