Expanding the left side:
(x-4)^2 - 6 = (x-4)(x-4) - 6= x^2 - 4x - 4x + 16 - 6= x^2 - 8x + 10
Expanding the right side:
(2+x)^2 = (2+x)(2+x)= 2*2 + 2x + 2x + x^2= 4 + 4x + x^2
Now we need to equate the two sides:
x^2 - 8x + 10 = 4 + 4x + x^2
Now, let's solve this equation:
x^2 - 8x + 10 = 4 + 4x + x^2=> -8x + 10 = 4 + 4x=> -8x - 4x = 4 - 10=> -12x = -6=> x = 1/2
Therefore, the solution to the equation is x = 1/2.
Expanding the left side:
(x-4)^2 - 6 = (x-4)(x-4) - 6
= x^2 - 4x - 4x + 16 - 6
= x^2 - 8x + 10
Expanding the right side:
(2+x)^2 = (2+x)(2+x)
= 2*2 + 2x + 2x + x^2
= 4 + 4x + x^2
Now we need to equate the two sides:
x^2 - 8x + 10 = 4 + 4x + x^2
Now, let's solve this equation:
x^2 - 8x + 10 = 4 + 4x + x^2
=> -8x + 10 = 4 + 4x
=> -8x - 4x = 4 - 10
=> -12x = -6
=> x = 1/2
Therefore, the solution to the equation is x = 1/2.