Answer:
6 or 0
Explanation:
To solve the quadratic equation \(9x(x-6) = 81\) by completing the square, follow these steps:
1. Expand the equation:
\[ 9x^2 - 54x = 81 \]
2. Move the constant term to the other side of the equation:
\[ 9x^2 - 54x - 81 = 0 \]
3. Divide the entire equation by the coefficient of \(x^2\), which is 9, to make the coefficient 1:
\[ x^2 - 6x - 9 = 0 \]
4. Now, complete the square. Take half of the coefficient of \(x\) (-6), square it, and add it to both sides of the equation:
\[ x^2 - 6x + (-6/2)^2 - 9 + (-6/2)^2 = (-6/2)^2 \]
\[ x^2 - 6x + 9 - 9 + 9 = 9 \]
5. Simplify:
\[ (x - 3)^2 = 9 \]
6. Take the square root of both sides:
\[ x - 3 = \pm 3 \]
7. Solve for \(x\):
\[ x = 3 \pm 3 \]
So, the solutions are \(x = 6\) or \(x = 0\).