Rewrite the equation by completing the square. 4x^2-12x+9=0 (x+-3)^2=0

To rewrite the equation by completing the square, we need to follow these steps:<br /><br />1. Move the constant term to the other side of the equation:<br />$4x^{2}-12x=-9$<br /><br />2. Divide the entire equation by the coefficient of $x^2$, which is 4:<br />$x^{2}-3x=-\frac{9}{4}$<br /><br />3. Take half of the coefficient of $x$, which is -3, and square it:<br />$\left(\frac{-3}{2}\right)^{2}=\frac{9}{4}$<br /><br />4. Add and subtract this value to the left side of the equation:<br />$x^{2}-3x+\frac{9}{4}=-\frac{9}{4}+\frac{9}{4}$<br /><br />5. Rewrite the left side as a perfect square:<br />$\left(x-\frac{3}{2}\right)^{2}=0$<br /><br />Therefore, the equation $4x^{2}-12x+9=0$ can be rewritten as $\left(x-\frac{3}{2}\right)^{2}=0$.