a)
\(3x^2+12x-66=0\)
\(\Leftrightarrow x^2+4x-22=0\)
\(\Leftrightarrow x^2+4x+4=26\Leftrightarrow (x+2)^2=26\)
\(\Rightarrow x+2=\pm \sqrt{26}\Rightarrow x=-2\pm \sqrt{26}\)
b)
\(9x^2-30x+225=0\)
\(\Leftrightarrow (3x)^2-2.3x.5+25+200=0\)
\(\Leftrightarrow (3x-5)^2=-200< 0\) (vô lý nên pt vô nghiệm)
c)
\(x^2+3x-10=0\)
\(\Leftrightarrow x^2-2x+5x-10=0\)
\(\Leftrightarrow x(x-2)+5(x-2)=0\Leftrightarrow (x+5)(x-2)=0\)
\(\Rightarrow x=-5\) hoặc $x=2$
d)
$3x^2-7x+1=0$
$\Leftrightarrow 3(x^2-\frac{7}{3}x)+1=0$
$\Leftrightarrow 3(x^2-\frac{7}{3}x+\frac{7^2}{6^2})=\frac{37}{12}$
$\Leftrightarrow 3(x-\frac{7}{6})^2=\frac{37}{12}$
$\Leftrightarrow (x-\frac{7}{6})^2=\frac{37}{36}$
$\Rightarrow x-\frac{7}{6}=\frac{\pm \sqrt{37}}{6}$
$\Rightarrow x=\frac{7\pm \sqrt{37}}{6}$
e)
$3x^2+7x+2=0$
$\Leftrightarrow 3(x^2+\frac{7}{3}x+\frac{7^2}{6^2})=\frac{25}{12}$
$\Leftrightarrow 3(x+\frac{7}{6})^2=\frac{25}{12}$
$\Leftrightarrow (x+\frac{7}{6})^2=\frac{25}{36}$
$\Rightarrow x+\frac{7}{6}=\pm \frac{5}{6}$
$\Rightarrow x=\frac{-1}{3}$ hoặc $x=-2$
f)
$4x^2-12x+9=0$
$\Leftrightarrow (2x)^2-2.2x.3+3^2=0$
$\Leftrightarrow (2x-3)^2=0\Rightarrow 2x-3=0\Rightarrow x=\frac{3}{2}$
g) Trùng câu e
h)
$x^2-4x+1=0$
$\Leftrightarrow x^2-4x+4-3=0$
$\Leftrightarrow (x-2)^2=3\Rightarrow x-2=\pm \sqrt{3}$
$\Rightarrow x=2\pm \sqrt{3}$
i)
$2x^2-6x+1=0$
$\Leftrightarrow 2(x^2-3x+\frac{3^2}{2^2})=\frac{7}{2}$
$\Leftrightarrow 2(x-\frac{3}{2})^2=\frac{7}{2}$
$\Leftrightarrow (x-\frac{3}{2})^2=\frac{7}{4}$
$\Rightarrow x-\frac{3}{2}=\pm \frac{\sqrt{7}}{2}$
$\Rightarrow x=\frac{3\pm \sqrt{7}}{2}$
j)
$3x^2+4x-4=0$
$\Leftrightarrow 3x^2+6x-2x-4=0$
$\Leftrightarrow 3x(x+2)-2(x+2)=0$
$\Leftrightarrow (x+2)(3x-2)=0$
$\Rightarrow x+2=0$ hoặc $3x-2=0$
$\Rightarrow x=-2$ hoặc $x=\frac{2}{3}$
