Question 282914
I'll do the first one to show you how to do these problems.





{{{x^2-2x-24}}} Start with the given expression.



Take half of the {{{x}}} coefficient {{{-2}}} to get {{{-1}}}. In other words, {{{(1/2)(-2)=-1}}}.



Now square {{{-1}}} to get {{{1}}}. In other words, {{{(-1)^2=(-1)(-1)=1}}}



{{{x^2-2x+highlight(1-1)-24}}} Now add <font size=4><b>and</b></font> subtract {{{1}}}. Make sure to place this after the "x" term. Notice how {{{1-1=0}}}. So the expression is not changed.



{{{(x^2-2x+1)-1-24}}} Group the first three terms.



{{{(x-1)^2-1-24}}} Factor {{{x^2-2x+1}}} to get {{{(x-1)^2}}}.



{{{(x-1)^2-25}}} Combine like terms.



So after completing the square, {{{x^2-2x-24}}} transforms to {{{(x-1)^2-25}}}. 



In other words, {{{x^2-2x-24=(x-1)^2-25}}}.