\(a,4x^2-49=0\\ \Leftrightarrow\left(2x-7\right)\left(2x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\\ b,x^2+36=12x\\ \Leftrightarrow x^2-12x+36=0\\ \Leftrightarrow\left(x-6\right)^2=0\\ \Leftrightarrow x=6\\ c,\dfrac{1}{16}x^2-x+4=0\\ \Leftrightarrow\left(\dfrac{1}{4}x-2\right)^2=0\\ \Leftrightarrow\dfrac{1}{4}x-2=0\\ \Leftrightarrow x=8\\ d,x^3-3\sqrt{3}x^2+9x-3\sqrt{3}=0\\ \Leftrightarrow\left(x-\sqrt{3}\right)^3=0\\ \Leftrightarrow x=\sqrt{3}\)
a. 4x2 - 49 = 0
<=> (2x2) - 72 = 0
<=> (2x - 7)(2x + 7) = 0
<=> \(\left[{}\begin{matrix}2x-7=0\\2x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=\dfrac{-7}{2}\end{matrix}\right.\)
b. x2 + 36 = 12x
<=> x2 - 12x + 36 = 0
<=> x2 - 6x - 6x + 36 = 0
<=> x(x - 6) - 6(x - 6) = 0
<=> (x - 6)(x - 6) = 0
<=> x - 6 = 0
<=> x = 6
