First, we need to rearrange the equation into a quadratic. A quadratic equation will always have a squared element.
To this, we move everything over to the left hand side of the equation and set it equal to zero. (Remember: Change the side, change the sign)
So..
x^2 = 2x - 1
becomes..
x^2 - 2x = - 1
and then..
x^2 - 2x + 1 = 0
One way to solve this equation is by using factorisation.
the equation takes the form.. ax2 + bx + c = 0
we need to find two numbers that add together to make be and multiply together to make a x c.
So, numbers that add to -2 and multiply to 1 x 1 = 1.
These numbers are -1 and -1.
So we can factorise the equation.
Step 1..
x2 - x - x - 1 = 0
Step 2..
x(x-1) - 1(x-1) = 0
Step 3..
(x-1)(x-1) = 0
So to find x, we simply divide both sides of the equation by (x-1).
Leaving x - 1 = 0, so x = 1.