I need help with this equation x(2x+1)=1?

Question

I need help with this question, the entire process would be really helpful more than the answer itself!

Answer 1

First, we expand the brackets:

2x^2 + x = 1

Then we shift everything on the same side:

2x^2+x-1=0

Then you can factorise the equation:

(2x-1)(x+1) = 0

either of these brackets can equal zero.

2x - 1 = 0; 2x = 1; x = 0.5

x + 1 = 0; x = -1

Therefore x = 0.5 and -1