Use completing the square to solve for x in the equation (x+7)(x-9)=25x = –4 or 6x = –2 or 14x = 1 ± sqrt(89)x = 1 ± sqrt(87)

First, we need to expand the left hand side expression:

[tex](x+7)(x-9)=x^2-9x+7x-63=x^2-2x-63.[/tex]

The quadratic and linear terms [tex]x^2-2x[/tex] are 'produced' from the expansion of the binomial [tex](x-1)^2[/tex] which is [tex]x^2-2x+1[/tex].


Thus, we can write [tex]x^2-2x-63[/tex] as [tex](x^2-2x+1)-64[/tex], which is equal to 
                                [tex](x-1)^2-64.[/tex]

     
Thus, the equation is [tex](x-1)^2-64=25[/tex]. Adding 64 to both sides, we have:
                                        [tex](x-1)^2=89[/tex].

 This means that x-1 is either [tex] \sqrt{89} [/tex] or [tex] -\sqrt{89} [/tex].

Finally, we see that x is either [tex]1+ \sqrt{89} [/tex] or [tex]1 -\sqrt{89} [/tex].


Answer: x = 1 ± sqrt(89)