Using completing the square solve for x

X^2-10x-9=0

X^2 - 10x - 9 = 0

first we will move the constant term to the other side

x^2 - 10x = 9

then, to both sides we will add the number that makes the polynomial on the left a perfect square trinomial. Take half of the coefficient of x, then square it. half of the coefficient of x (-10) is - 5, and - 5 squared is 25. so:

x^2 - 10x + 25 = 34

factor the perfect square trinomial

(x - 5) ^2 = 34

x - 5 = plus or minus sqrt (34)

x = 5 plus or minus sqrt (34)