\(x^2+7x+8=0\)
\(\Rightarrow x^2+7x+\dfrac{49}{4}-\dfrac{17}{4}=0\)
\(\Rightarrow\left(x+\dfrac{7}{2}\right)^2-\dfrac{17}{4}=0\)
\(\Rightarrow\left(x+\dfrac{7}{2}+\sqrt{\dfrac{17}{4}}\right)\left(x+\dfrac{7}{2}-\sqrt{\dfrac{17}{4}}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-\sqrt{\dfrac{17}{4}}-\dfrac{7}{2}\\x=\sqrt{\dfrac{17}{4}}-\dfrac{7}{2}\end{matrix}\right.\)
x2 + 7x + 8 = 0
x2 + 7x = 0 - 8
x2 + 7x = -8
Đặt \(\left(\dfrac{b}{2}\right)^2=\left(\dfrac{7}{2}\right)^2\)
\(\Rightarrow\) x2 + 7x + \(\left(\dfrac{7}{2}\right)^2\) = ( -8 ) + \(\left(\dfrac{7}{2}\right)^2\)
\(\Rightarrow\) x2 + 7x + \(\left(\dfrac{7}{2}\right)^2\) = ( -8 ) + \(\dfrac{49}{4}\)
\(\Rightarrow\) x2 + 7x + \(\dfrac{49}{4}=\dfrac{17}{4}\)
\(\Rightarrow\) ( x + \(\dfrac{7}{2}\) )2 = \(\dfrac{17}{4}\)
( x + \(\dfrac{7}{2}\) )2.1/2 = \(\pm\sqrt{\dfrac{81}{4}}\)
( x + \(\dfrac{7}{2}\) ) = \(\pm\) \(\sqrt{\dfrac{81}{4}}\)
( x + \(\dfrac{7}{2}\) ) = \(\pm\) \(\dfrac{\sqrt{81}}{\sqrt{4}}\)
( x + \(\dfrac{7}{2}\) ) = \(\pm\) \(\dfrac{9}{2}\)
\(\left\{{}\begin{matrix}x+\dfrac{7}{2}=\dfrac{9}{2}\\x+\dfrac{7}{2}=\dfrac{-9}{2}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{9}{2}-\dfrac{7}{2}\\x=\dfrac{-9}{2}-\dfrac{7}{2}\end{matrix}\right.\)
\(\Rightarrow\) \(\left\{{}\begin{matrix}x=1\\x=-8\end{matrix}\right.\)
Vậy x = 1 hoặc x = -8
