Answer: (x - 4)² - 25
Step-by-step explanation:
[tex]{ \boxed{ \tt{ \: {x}^{2} - 4x - 21 \: }}}[/tex]
» Let us use completing perfect squares to find the final expression.
☑ When completing squares, we first find the "square of the half of the sum"
[tex]{ \boxed{ \tt{square \: of \: sums \: half = {( \frac{ - 4}{2} )}^{2} = {( - 2)}^{2} = 4 }}}[/tex]
» Then we add the result to x² and -21
[tex] = { \tt{( {x}^{2} - 4x + 4) + ( - 21 - 4) }} \\ = { \tt{ {(x - 2)}^{2} - 25 }}[/tex]
