Solve x^2 = 4(x – 3)^2
To solve this equation we need to firast expand it.
x2=4(x-3)2
To do this we first expand the brackets. Remeber anything squared means times it by itself
(x-3)2
=(x-3)(x-3)
=x2-6x+9
This makes the equation look like this
x2=4(x2-6x+9)
We know times the brakcet out by the 4 to give us
x2=4x2-24x+36
To solve this question we need to find x, to this we can see that we can minus x2 from both sides
0=3x2-24x+36
we can divide this equation by 3 to give us
0=x2-8x+12
Now to factorise this equation we need to find two numbers that multiply together to make twelve and add together to make -8. This shows us that
0=x2-2x-6x+12
0=x(x-2)-6(x-2)
0=(x-2)(x-6)
Becasue the equation equals 0 we can see that
0=(x-2) 0=(x-6)
0=x-2 0=x-6
x=2 x=6
Thus the solution to x2=4(x-3)2 is x=2 or x=6
