Question 978593


1. Rewrite your equation as 


{{{x^2 - 5x - 2}}} = {{{0}}}.


2. Complete the square for the polynomial in the left side


{{{x^2 -5x - 2}}} = {{{(x-5/2)^2}}} - {{{(5/2)^2}}} - {{{2}}} = {{{(x-5/2)^2}}} - {{{25/4}}} - {{{2}}} = {{{(x-5/2)^2}}} - {{{(25 + 2*4)/4}}} = {{{(x-5/2)^2}}} - {{{33/4}}}.


3. Now your equation is 


{{{(x-5/2)^2}}} - {{{33/4}}} = {{{0}}}.


4. Rewrite it in the form


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


5. Take the square root in both sides:


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


6. Now {{{x}}} = {{{5/2}}} +/- {{{sqrt(33)/2}}}.


You got two roots. Congratulations!