Question

Complete the square for 3x² - 12x = 9.OA. (3x-2)2 = 20OB. (x + 2)² = 7OC. (x-2)² = 7OD. (3x-2)2 = 13what letter is it

Answer 1

The equation is given to be:

`3x^2-12x=9`

Divide each term by 3:

`\begin{gathered} (3x^2)/(3)-(12x)/(3)=(9)/(3) \\ x^2-4x=3 \end{gathered}`

Add the square of half the coefficient of x to both sides of the equation:

`\begin{gathered} Coefficient=-4 \\ Half=-(4)/(2)=-2 \\ Square=(-2)^2 \\ \therefore \\ x^2-4x+(-2)^2=3+(-2)^2 \\ x^2-4x+(-2)^2=7 \end{gathered}`

Complete the square:

`(x-2)^2=7`

The correct option is OPTION C.