(2x-3)^2 = 4x^2 - 12x + 9(a^2+4)^2 = a^4 + 8a^2 + 16(2c-1)^2 = 4c^2 - 4c + 1
Therefore:(2x-3)^2 = (a^2+4)^2 - 16a^2 = 9 - (2c-1)^24x^2 - 12x + 9 = a^4 + 8a^2 + 16 - 16a^2 = 9 - (4c^2 - 4c + 1)4x^2 - 12x + 9 = a^4 - 8a^2 + 16 = 10 - 4c^2 + 4c4x^2 - 12x + 9 = a^4 - 8a^2 + 16 = 4c^2 - 4c + 10
Finally, 1-(2x-3)^2=(a^2+4)^2-16a^2=9-(2c-1)^2 simplifies to:1 - (4x^2 - 12x + 9) = (a^4 + 8a^2 + 16) - 16a^2 = 9 - (4c^2 - 4c + 1)1 - 4x^2 + 12x - 9 = a^4 + 8a^2 + 16 - 16a^2 = 9 - 4c^2 + 4c - 1-4x^2 + 12x - 8 = a^4 - 8a^2 + 16 = 8 - 4c^2 + 4c
Therefore, the simplified equation is:-4x^2 + 12x - 8 = a^4 - 8a^2 + 16 = 8 - 4c^2 + 4c
(2x-3)^2 = 4x^2 - 12x + 9
(a^2+4)^2 = a^4 + 8a^2 + 16
(2c-1)^2 = 4c^2 - 4c + 1
Therefore:
(2x-3)^2 = (a^2+4)^2 - 16a^2 = 9 - (2c-1)^2
4x^2 - 12x + 9 = a^4 + 8a^2 + 16 - 16a^2 = 9 - (4c^2 - 4c + 1)
4x^2 - 12x + 9 = a^4 - 8a^2 + 16 = 10 - 4c^2 + 4c
4x^2 - 12x + 9 = a^4 - 8a^2 + 16 = 4c^2 - 4c + 10
Finally, 1-(2x-3)^2=(a^2+4)^2-16a^2=9-(2c-1)^2 simplifies to:
1 - (4x^2 - 12x + 9) = (a^4 + 8a^2 + 16) - 16a^2 = 9 - (4c^2 - 4c + 1)
1 - 4x^2 + 12x - 9 = a^4 + 8a^2 + 16 - 16a^2 = 9 - 4c^2 + 4c - 1
-4x^2 + 12x - 8 = a^4 - 8a^2 + 16 = 8 - 4c^2 + 4c
Therefore, the simplified equation is:
-4x^2 + 12x - 8 = a^4 - 8a^2 + 16 = 8 - 4c^2 + 4c