For this case, we must find the quadratic equation equivalent to:
[tex](x-4) ^ 2- (x-4) -6 = 0[/tex]
By definition we have to:
[tex](a-b) ^ 2 = a^2-2ab + b ^ 2[/tex]
So:
[tex](x-4) ^ 2 = x ^ 2-2 (x) (4) + 4 ^ 2 = x ^ 2-8x + 16[/tex]
So, we have:
[tex]- * + = +\\- * - = +[/tex]
[tex]x ^ 2-8x + 16-x + 4-6 = 0[/tex]
Equal signs add up and the same sign is placed.
Different signs are subtracted and the sign of the major is placed.
[tex]x ^ 2-9x + 14 = 0[/tex]
Answer:
[tex]x ^ 2-9x + 14 = 0[/tex]
