Question

hi pls find x. i can't seem to factor it.

3x^2 +7x = x -2

Answer 1

This can be simplified to:
3x^2 + 6x + 2 = 0
If all else fails, we can always use the quadratic formula, or:
We divide the entire thing by 3:
x^2 + 2x + (2/3) = 0
And then, we complete the square:
x^2 + 2x + (2/3) + 1 - 1= 0 ---> (we added 1 and then subtracted 1, effectively nullifying)

(x^2 + 2x + 1) + (2/3) - 1 = 0
(x + 1)^2 - (1/3) = 0
x + 1 = sqrt(1/3)
x = -1 - sqrt(1/3) OR x = -1 + sqrt(1/3)

Answer 2

\[3x^2+7x=x-2\]
\[3x^2+7x-x+2=0\]
\[3x^2+6x+2=0\]
We can't factorise this so quadratic formula ahoy!
Where:
a=3
b=6
c=2

\[x=(-b \pm \sqrt{b^2-4ac})/2a\]
\[x=(-6\pm \sqrt{6^2-4(3)(2)})/6\]
\[x=(-6\pm \sqrt{12})/6\]
\[x=(-6\pm2\sqrt{3})/6\]
\[x=(-3\pm \sqrt{3})/3\]
\[x=-1\pm \sqrt{3}/3\]

Hope that helps :)