Which of the following equations is the result of completing the square on x² - 6x - 9 = 0?

Solution:

A quadratic equation is in the form of ax² + bx + c = 0. To find the roots of the quadratic equation, we can use completing the square method.

Let's find the solution step by step.

Step 1: Rearrange the equation in the form of ax² + bx = c, 

⇒ x² - 6x = 9 

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

⇒ x² - 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 x² - 6x - 9 = 0 is 3 + 3√2 or 3 - 3√2 by completing the square method.

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Which of the following equations is the result of completing the square on x² - 6x - 9 = 0?

Summary:

The set of solutions for the equation x² - 6x - 9 = 0 is 3 + 3√2 or 3 - 3√2 by completing the square method.