x= -2 or x= 8
Step-by-step explanation:
![x^{2} - 6x + 9 = 25](/tpl/images/0544/0902/8fb97.png)
First step, move 25 to the left side so we can do the Quadratic Formula (or you can factor instead.)
![x^{2} -6x + 9 - 25 = 0](/tpl/images/0544/0902/3ae50.png)
Next, we know that 9-25 equals -16.
![x^{2} - 6x - 16 = 0](/tpl/images/0544/0902/20606.png)
Now find that what two numbers multiply and get 16: 2×8 4×4 and 16×1.
Now we do some kind of factoring. The most valuable number must be negative since -6x is negative.
Let's explain about factoring in Quadratic a little bit.
Substitue x²-6x-16 as ax²+bx+c=0
From (ax+d)(bx+c), if we multiply ax and bx, we get the ax²
If we multiply ax and c, we get acx and we multiply d and bx, we get dbx. (axc+bdx) = bx
If we multiply d and c, we get c.
From the factor lf 16, 2×8 seems to be right since -8+2 equals -6 which matches the equation.
Then we get.
![(x - 8)(x + 2) = 0](/tpl/images/0544/0902/5a721.png)
Seperate both equations.
![x - 8 = 0 \\ x + 2 = 0](/tpl/images/0544/0902/9a8c5.png)
Find the value of both x.
![x = 8 \\ x = - 2](/tpl/images/0544/0902/b48ff.png)
The answer is x = -2, 8
(The explanation might be weird since I don't know what they are called in English.)