Odpowiedź:
1.
a)
[tex]-7x^{2}+42x=0 \\ -7x(x-6)=0 \\x=0 \;,\;x=6[/tex]
b)
[tex]9x^{2}+\frac{1}{3}x=0 \\ x(9x+\frac{1}{3})=0 \\ x=0 \;,\;x=-\frac{1}{27}[/tex]
c)
[tex]36x^{2}=6x \\ 36x^{2}-6x=0 \\6x(6x-1)=0 \\ x=0 \;,\;x=\frac{1}{6}[/tex]
d)
[tex]2x+18x^{2} = 0 \\ 2x(1+9x) = 0 \\ x=0 \;,\; x=-\frac{1}{9}[/tex]
2.
a)
[tex]100x^{2}-81=0\\x^{2}=\frac{81}{100}\\x=-\frac{9}{10} \;,\;x=\frac{9}{10}[/tex]
b)
[tex]\frac{1}{4}x^{2}-\frac{1}{9}=0\\x^{2}=\frac{4}{9}\\x=-\frac{2}{3}\;,\;x=\frac{2}{3}[/tex]
c)
[tex]x^{2}+10x+25=0\\(x+5)^{2}=0\\x=-5[/tex]
d)
[tex]x^{2}+64=16x\\x^{2}-16x+64=0\\(x-8)^{2}=0\\x=8[/tex]
e)
[tex]24x-x^{2}=144\\x^{2}-24x+144=0\\(x-12)^{2}=0\\x=12[/tex]
f)
[tex]1+9x^{2}+6x=0\\(3x+1)^{2}=0\\x=-\frac{1}{3}[/tex]
Szczegółowe wyjaśnienie:
