Question 172883
Step 1:  Arrange your equation so that the variables are on the left and the constant term is on the right:


{{{x^2=5x+2}}} => {{{x^2-5x=2}}}


Step 2:  Divide both sides by the coefficient on the 2nd order term.  In this case the coefficient is 1, so you can ignore this step.


Step 3:  Divide the coefficient on the 1st order term by 2 and then square the result.


{{{(5/2)^2=25/4}}}


Step 4:  Add the result of Step 3 to both sides of the equation


{{{x^2+5x+(25/4)=2+(25/4)}}}


Step 5:  You have now created a perfect square trinomial on the left.  Factor it


{{{(x+(5/2))^2=33/4}}}


Step 6:  Take the square root of both sides remembering to consider both the positive and negative roots


{{{x+(5/2)=sqrt(33/4)}}} or {{{x+(5/2)=-sqrt(33/4)}}}


{{{x[1]=(-5+sqrt(33))/2}}} or {{{x[2]=(-5-sqrt(33))/2}}}


Those are the exact answers.  You can use a calculator if you need numerical approximations