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

Question

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

campbell_st · Answer

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.

drewkatski · Answer

so then I get (x-7)^2 - 225 ?
which is the complete square form i think and how do I factorize that?

campbell_st · Answer

well now you have the difference of 2 squares

$$a^2 - b^2 = (a -b)(a + b)$$

campbell_st · Answer

so it depends on how far you need to go in factoring the quadratic expression

drewkatski · Answer

wait I dont understand do i keep (x-7) and in the other bracket put (x+[sq root of 225]) ?

campbell_st · Answer

you can... this is an expression and not an equation... is that correct..?

campbell_st · Answer

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

drewkatski · Answer

I just checked the answer section and I saw that the answer is (x-22) (x+8) 
so im confused a bit

campbell_st · Answer

well now if you factor as the difference of 2 squares you get

$$((x -7) + 15)((x -7) - 15)$$

just simplify it

campbell_st · Answer

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

drewkatski · Answer

I understand!! Thank you so much mate :)
haha I find many steps to be pointless but I just follow the teacher
thank you again!