\(x^2+5x-14=0\)
\(\Leftrightarrow x^2-2x+7x-14=0\)
\(\Leftrightarrow x\left(x-2\right)+7\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-7\end{matrix}\right.\)
Vậy pt đã cho có nghiệm là \(x\in\left\{2;-7\right\}\).
\(\Delta=5^2-4\cdot1\cdot\left(-14\right)=25+56=81>0\)
\(\Rightarrow\) PT có 2 nghiệm phân biệt
\(x_1=\dfrac{-5+\sqrt{81}}{2}=\dfrac{-5+9}{2}=2\)
\(x_2=\dfrac{-5-\sqrt{81}}{2}=\dfrac{-5-9}{2}=-7\)
Vậy S = \(\left\{2;-7\right\}\)
\(x^2+5x-14=0\)
\(\Leftrightarrow x^2+5x=14\)
\(\Leftrightarrow x\left(x+5\right)=14\)
\(\Leftrightarrow x^2=9\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=3\end{matrix}\right.\)