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Using the method of completing the square, rewrite x² – 14x in the form (x + b)2 +c.
x2 – 14x = x(x - 14)
x² – 14x =

Using the method of completing the square rewrite x 14x in the form x b2 c x2 14x xx 14 x 14x class=

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LammettHash

If you want to have

[tex]x^2-14x = (x+b)^2+c[/tex]

notice that expanding the right side gives

[tex]x^2-14x = x^2+2bx+b^2+c[/tex]

so that

[tex]\begin{cases}2b=-14 \\ b^2+c=0\end{cases}[/tex]

It follows that b = -7 and c = -49. Then

[tex]x^2-14x = \boxed{(x-7)^2-49}[/tex]

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