Answer:
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
