Question

4 x^{2} -12 x +9 = 0
Rewrite the equation by completing the square.

Answer 1

Explanation:

`4x^2-12x+9=0\\4*9=36\\6+6=12\\6*6=36\\4x^2-(6+6)x+9=0\\4x^2-6x-6x+9=0\\2x(2x-3)-3(2x-3)=0\\(2x-3)(2x-3)=0\\(2x-3)^2=0`

Answer 2

`(x-(3)/(2)) ^(2)`

Explanation:

When we complete the square, we take the b value from the equation:

a
`x^(2)` + bx + c = 0, and plug it into
`((b)/(2))^(2)` ..

First step is to make the coefficent of x go away. By dividing by 4.

x^2 - 3x + 9/4 = 0

now plug into the equation

(-3/2)^2 = 9/4 <-- because the square is parantheses, the negative goes away. Notice how there is a 9/4 already in our equation, meaning we dont have to do anything and simply can find the answer!

(x - 3/2)^2 = 0