Question

Complete the square for 3x^2-12x=9

Answer 1

Answer:

The solutions are -0.65 and 4.65.

Step-by-step explanation:

3x^2 - 12x = 9

Divide both sides by 3

x^2 - 4x = 3

To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2.  So add 4 to both sides.

x^2 - 4x + 4 = 7

(x-2)^2 = 7

x - 2 = (square root) of 7

x = 2 (+/-) (square root) of 7.

x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

hope this helps:)sorry if it doesnt

Answer 2

Answer:

$(x-2)^2=7$

Step-by-step explanation:

We have been given an equation $3x^2-12x=9$. We are asked to complete the square for the given equation.

We know that when an equation is in form $x^2+bx=c$, then we will add $(\frac{b}{2})^2$ to both sides of equation to make a perfect square.

Dividing both sides by 3, we will get:

$x^2-4x=3$

Add $(\frac{b}{2})^2$ on both sides of equation:

$(\frac{b}{2})^2=(\frac{4}{2})^2=2^2=4$

$x^2-4x+4=3+4$

$x^2-4x+4=7$

Now, apply perfect square formula $a^2-2ab+b^2=(a-b)^2$:

$(x-2)^2=7$

Therefore, our required equation would be $(x-2)^2=7$.