If \[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $c.$

asked Feb 25, 2024 190k views

2 votes

If
\[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $c.$

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4 votes

Answer:

Explanation:

x^(2) -7x+c=(x+a)^(2)

x^(2) -7x+c=x^(2) +2ax+a^(2)

$-7x=2ax\\a=-7/2$

$a^(2) =c\\c=(-7/2)^(2) =49/4$

PriceHardman answered Mar 2, 2024