C1: \(2x^2+5x+3=0\)
\(\Leftrightarrow\left(2x^2+2x\right)+\left(3x+3\right)=0\)
\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+3=0\\x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{-3}{2}\\x=-1\end{cases}}\)
C2 : \(2x^2+5x+3=0\)
\(\Leftrightarrow2\left(x^2+\frac{5}{2}x+\frac{25}{16}\right)-\frac{1}{8}=0\)
\(\Leftrightarrow2\left(x+\frac{5}{4}\right)^2=\frac{1}{8}\)
\(\Leftrightarrow\left(x+\frac{5}{4}\right)^2=\frac{1}{16}\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{5}{4}=\frac{1}{4}\\x+\frac{5}{4}=-\frac{1}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-\frac{3}{2}\end{cases}}\)
Vậy ...
C1 : \(x^2+6x-16=0\)
\(\Leftrightarrow\left(x^2-2x\right)+\left(8x-16\right)=0\)
\(\Leftrightarrow x\left(x-2\right)+8\left(x-2\right)=0\)
\(\Leftrightarrow\left(x+8\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+8=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-8\\x=2\end{cases}}\)
C2 : \(x^2+6x-16=0\)
\(\Leftrightarrow\left(x^2+6x+9\right)-25=0\)
\(\Leftrightarrow\left(x+3\right)^2-5^2=0\)
\(\Leftrightarrow\left(x+3+5\right)\left(x+3-5\right)=0\)
\(\Leftrightarrow\left(x+8\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+8=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-8\\x=2\end{cases}}\)
Vậy ...
