Answer:
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)
