1.x² - 5x + 1 = 0

First you have to divide the equation by a the simplify. But its already simplified so let's move to next step.The variables should stay on the left side and move the constant term to the other side then the sign of it w\should be changed.

x² - 5x= -1

Add the square of 1/2 of the coefficient of x on both sides of the resulting equation. This means, you need to add square of the half of the value of b (ax
²+bx+c=0) on both sides of the equation.

Half of 5 is 5/2 and the square of it was 25/4 so the equation would be like this:

Simplify the equation.


The left side of the equation becomes perfect square trinomial. Express the square binomial on the left side of equation as a square of binomial.


Then extract the square roots:
 \sqrt{(x-5) ^{2} }   =  \sqrt{21/4}
x-5= positive or negative  \sqrt{21}

x= \sqrt{21}/4 + 5
x=- \sqrt{21}/4 + 5

I hope you can solve now the no. 2. But this is the answer:
x= \sqrt{10} /3 +2/3

x=- \sqrt{10} /3 +2/3
1 5 1
Woah~ thanks a lot. But I also need a solution for no. 2. No need for the explanations.