What are the roots of the equation X squared plus 6X - 9 equals zero?

x = - 3 + 2√3 and

x = - 3 - 2√3)

Step-by-step explanation:

x² + 6x - 9 = 0 can be solved in a variety of ways. Here I'll "complete the square" to solve for x:

x² + 6x - 9 = 0 can be re-written as x² + 6x + 9 - 9 - 9 = 0. To do this, we identify the coefficient of x (which is 6), halve it (obtaining 3), square the result (obtaining 9), and then add and then subtract this result (9) between 6x - 9.

Simplifying x² + 6x + 9 - 9 - 9 = 0 results in:

(x + 3) ² = 18

Taking the square root of both sides, we get:

x + 3 = ±√18) = ±3√2

Solving this for the two roots, we get:

x = - 3 + 2√3 and

x = - 3 - 2√3)