What is are the steps to factoring - x^2 + 6x - 9

Step-by-step explanation:

-x^2 + 6x - 9

The first step is to find the coefficient of x^2 (i. e. the num in front of x^2) = - 1

The constant is - 9

Therefore, the product of the equation = - 1 x - 9 = + 9

Sum of the equation = the coefficient of x = + 6

Then, we look for two factors (numbers) whose product = + 9, and sum = + 6

What of + 3 and + 3?

+3 + 3 = + 6

+3 x + 3 = + 9

Therefore, + 3 and + 3 are the factors of the equation.

We then substitute the sum of the equation (+6x) with these factors.

So, we have,

-x^2 + 3x + 3x - 9

We then pair the equation and equate to Zero

(-x^2 + 3x) (+3x - 9) = 0

Common factor in the first pair is - x and + 3 in the second.

-x (x - 3) + 3 (x - 3) = 0

At this stage, same factor must be in the bracket (i. e. x-3)

So, we now have,

(-x + 3) (x-3) = 0

We equate each to zero

-x + 3 = 0 and x-3=0

-x = - 3. and x = + 3

x = + 3 and x = + 3

Therefore, x = + 3 and + 3