Please help me with this pure math question, much appreciated :) Make the following into complete square form then factorize: x^2 - 14x - 176

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Please help me with this pure math question, much appreciated :) Make the following into complete square form then factorize: x^2 - 14x - 176

Mathematics
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so group the terms in x \[(x^2 - 14x + ?) -176 - ?\] so take halve of the coefficient of the term in x and then square it... add it inside the brackets and subtract it out side the brackets to keep the equation in balance.
so then I get (x-7)^2 - 225 ? which is the complete square form i think and how do I factorize that?
well now you have the difference of 2 squares \[a^2 - b^2 = (a -b)(a + b)\]

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so it depends on how far you need to go in factoring the quadratic expression
wait I dont understand do i keep (x-7) and in the other bracket put (x+[sq root of 225]) ?
you can... this is an expression and not an equation... is that correct..?
well if you complete the square you get \[(x -7)^2 - 15^2\] you ahve the difference of 2 square... so it can be factored and the linear factors can be simplified
I just checked the answer section and I saw that the answer is (x-22) (x+8) so im confused a bit
well now if you factor as the difference of 2 squares you get \[((x -7) + 15)((x -7) - 15)\] just simplify it
the question seems a little odd... as it could have been factored from the get go into these 2 linear factors with using complete the square
I understand!! Thank you so much mate :) haha I find many steps to be pointless but I just follow the teacher thank you again!

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