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:

$\begin{gathered} \frac{3x^2}{3}-\frac{12x}{3}=\frac{9}{3} \\ x^2-4x=3 \end{gathered}$

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

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

Complete the square:

$(x-2)^2=7$

The correct option is OPTION C.