What are the values of x in the equation x2 - 6x + 9 = 25?

x = - 2 or x = 8

x = - 1 or x = - 11

x = 1 or x = 11

x = 2 or x = - 8

x = - 2 or x = 8

Step-by-step explanation:

x²-6x+9 = 25

Subtracting 25 from both the sides,

x²-6x+9-25 = 25 - 25

Cancelling out 25 and - 25 from the right side

x²-6x+9-25 = 0

1x²-6x-16 = 0

Multiplying the quotient of the first term with the last term,

1 * (-16) = - 16

We need to find out two such factors of - 16 which when added gives us the middle term coefficient - 6.

-8 and 2 are such factors of - 16, which when added gives us the middle term coefficient - 6.

So, we rewrite the middle term - 6x as - 8x+2x

x²-8x+2x-16 = 0

Factor out x from the first two terms

x (x-8) + 2x-16 = 0

Factor out 2 from the last two terms

x (x-8) + 2 (x-8) = 0

Factor out (x-8) from both the terms

(x-8) (x+2) = 0

Either x-8 = 0 or x+2=0

Solving x-8=0, we get x = 8

Solving x+2=0, we get x = - 2

The answer is A, x = - 2 or x = 8