Question

Solve this quadratic equation by completing the square: x² − 6x = 18 a) x = - 3 ± √27 b) x = - 6 ± √18 c) x = - 6 ± √27 d) x = - 3 ± √27

Answer 1

The quadratic equation x^2 - 6x = 18 is solved by completing the square, resulting in the solutions x = 3 ± √27, which matches option (d).

Step-by-step explanation:

To solve the quadratic equation x² − 6x = 18 by completing the square, we will first move the constant term to the right side of the equation to set the equation equal to zero. Here's the step-by-step process:

1. Start with the equation x² − 6x = 18.
2. Subtract 18 from both sides to get x² − 6x − 18 = 0.
3. To complete the square, take the coefficient of the x term (which is -6), divide it by 2, and square the result to get 9. Then add and subtract this number inside the equation to get x² − 6x + 9 − 9 − 18 = 0.
4. Combine like terms to form a perfect square trinomial on the left side, resulting in (x − 3)² = 27.
5. Take the square root of both sides, yielding x − 3 = ±√27.
6. Finally, add 3 to both sides to isolate x, which gives us the solutions x = 3 ± √27.

Therefore, the correct answer is x = 3 ± √27, which corresponds to option (d).