# Which of the following equations is the result of completing the square on x^{2} - 6x - 9 = 0?

A quadratic equation is in the form of ax^{2 }+ bx + c = 0. To find the roots of the quadratic equation, we can use completing the square method.

## Answer: The set of solutions for the equation x^{2} - 6x - 9 = 0 is 3 + 3√2 or 3 - 3√2 by completing the square method.

Let's find the solution set that satisfies the equation.

**Explanation:**

Let's find the solution step by step.

Step 1: Rearrange the equation in the form of ax^{2 }+ bx = c,

⇒ x^{2} - 6x = 9

Step 2: Add (b / 2)^{2} on both the sides of the equation. Here, b = -6.

⇒ x^{2} - 6x + (-6 / 2)^{2 }= 9 + (-6 / 2)^{2}

Step 3: Factorize the sides using algebraic identity (a - b)^{2 }into perfect squares.

⇒ (x - 6 / 2)^{2} = 9 + (-3)^{2}

Step 4: By taking square root on both the sides,

⇒ √(x - 6 / 2)^{2} = √18

Step 5: Solve for x.

⇒ x - 3 = ± 3√2

⇒ x = ± 3√2 + 3

⇒ x = 3 + 3√2 or 3 - 3√2

We can solve the quadratic equation using Cuemath's online quadratic equation calculator.

### Thus, the set of solutions for the equation x^{2} - 6x - 9 = 0 is 3 + 3√2 or 3 - 3√2 by completing the square method.

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