Find the exact roots of x^2+10x-8=0 by completing the square

From the original equation x^2+10x-8=0, move the loose number on the other side. Your new equation will be x^2+10x=8. Moving an element from one side to another reverses its sign. From -8 to +8. Then take half of the x-term and square it and add it on both sides. X-term is 10x and 10 is the number, half of it is 5 then square of 5 is 25. Add 25 on both side. Your new equation will be x^2+10x+25=8+25. Then complete the square form of the left side of the equation, (x+5)^2=33. Square root both side then you will get x+5=squareroot of 33. Your x = -5 plus/minus squareroot of 33.