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:
[tex](x-2)^2=7[/tex]
Step-by-step explanation:
We have been given an equation [tex]3x^2-12x=9[/tex]. We are asked to complete the square for the given equation.
We know that when an equation is in form [tex]x^2+bx=c[/tex], then we will add [tex](\frac{b}{2})^2[/tex] to both sides of equation to make a perfect square.
Dividing both sides by 3, we will get:
[tex]x^2-4x=3[/tex]
Add [tex](\frac{b}{2})^2[/tex] on both sides of equation:
[tex](\frac{b}{2})^2=(\frac{4}{2})^2=2^2=4[/tex]
[tex]x^2-4x+4=3+4[/tex]
[tex]x^2-4x+4=7[/tex]
Now, apply perfect square formula [tex]a^2-2ab+b^2=(a-b)^2[/tex]:
[tex](x-2)^2=7[/tex]
Therefore, our required equation would be [tex](x-2)^2=7[/tex].
