a: \(x^2+x+\dfrac{1}{4}=\dfrac{9}{4}\)
=>\(x^2+x+\dfrac{1}{4}-\dfrac{9}{4}=0\)
=>\(x^2+x-2=0\)
=>(x+2)(x-1)=0
=>\(\left[{}\begin{matrix}x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)
b: \(25x^2-16\left(x+2\right)^2=0\)
=>\(\left(5x\right)^2-\left(4x+8\right)^2=0\)
=>(5x-4x-8)(5x+4x+8)=0
=>(x-8)(9x+8)=0
=>\(\left[{}\begin{matrix}x-8=0\\9x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{8}{9}\end{matrix}\right.\)
c: \(\left(2x+1\right)^2=\left(x-1\right)^2\)
=>\(\left(2x+1\right)^2-\left(x-1\right)^2=0\)
=>\(\left(2x+1+x-1\right)\left(2x+1-x+1\right)=0\)
=>\(3x\cdot\left(x+2\right)=0\)
=>x(x+2)=0
=>\(\left[{}\begin{matrix}x=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
d: \(9x^2-6x=-1\)
=>\(9x^2-6x+1=0\)
=>\(\left(3x-1\right)^2=0\)
=>3x-1=0
=>3x=1
=>\(x=\dfrac{1}{3}\)
e: \(4x^2-9=0\)
=>\(4x^2=9\)
=>\(x^2=\dfrac{9}{4}\)
=>\(\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
f: \(x^3-9x^2+27x-35=0\)
=>\(x^3-9x^2+27x-27-8=0\)
=>\(\left(x^3-9x^2+27x-27\right)=8\)
=>\(\left(x-2\right)^3=2^3\)
=>x-2=2
=>x=2+2=4
g: \(x^2-6x-7=0\)
=>\(x^2-7x+x-7=0\)
=>x(x-7)+(x-7)=0
=>(x-7)(x+1)=0
=>\(\left[{}\begin{matrix}x-7=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\)
