Whakaoti mō x (complex solution)
x\in \mathrm{C}
Whakaoti mō x
x\in \mathrm{R}
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Kua tāruatia ki te papatopenga
\left(\frac{7}{12}+\frac{245}{50}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{28}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{245}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Tāpirihia te 48 ki te 52, ka 100.
\left(\frac{7}{12}+\frac{49x}{10\times 100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Me whakarea te \frac{49}{10} ki te \frac{x}{100} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.
\left(\frac{7\times 250}{3000}+\frac{3\times 49x}{3000}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 12 me 10\times 100 ko 3000. Whakareatia \frac{7}{12} ki te \frac{250}{250}. Whakareatia \frac{49x}{10\times 100} ki te \frac{3}{3}.
\frac{7\times 250+3\times 49x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Tā te mea he rite te tauraro o \frac{7\times 250}{3000} me \frac{3\times 49x}{3000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.
\frac{1750+147x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Mahia ngā whakarea i roto o 7\times 250+3\times 49x.
\frac{1750+147x}{3000}\times 0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakareatia te 0 ki te 1, ka 0.
0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Ko te tau i whakarea ki te kore ka hua ko te kore.
0+\frac{4}{5}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
0+0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakareatia te \frac{4}{5} ki te 0, ka 0.
0+0+\frac{15}{30}\times 0\times 75=0\times 5
Whakareatia te 0 ki te 15, ka 0.
\frac{15}{30}\times 0\times 75=0\times 5
Tāpirihia te 0 ki te 0, ka 0.
\frac{1}{2}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{15}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 15.
0\times 75=0\times 5
Whakareatia te \frac{1}{2} ki te 0, ka 0.
0=0\times 5
Whakareatia te 0 ki te 75, ka 0.
0=0
Whakareatia te 0 ki te 5, ka 0.
\text{true}
Whakatauritea te 0 me te 0.
x\in \mathrm{C}
He pono tēnei mō tētahi x ahakoa.
\left(\frac{7}{12}+\frac{245}{50}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{28}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{245}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Tāpirihia te 48 ki te 52, ka 100.
\left(\frac{7}{12}+\frac{49x}{10\times 100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Me whakarea te \frac{49}{10} ki te \frac{x}{100} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.
\left(\frac{7\times 250}{3000}+\frac{3\times 49x}{3000}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 12 me 10\times 100 ko 3000. Whakareatia \frac{7}{12} ki te \frac{250}{250}. Whakareatia \frac{49x}{10\times 100} ki te \frac{3}{3}.
\frac{7\times 250+3\times 49x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Tā te mea he rite te tauraro o \frac{7\times 250}{3000} me \frac{3\times 49x}{3000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.
\frac{1750+147x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Mahia ngā whakarea i roto o 7\times 250+3\times 49x.
\frac{1750+147x}{3000}\times 0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakareatia te 0 ki te 1, ka 0.
0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Ko te tau i whakarea ki te kore ka hua ko te kore.
0+\frac{4}{5}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
0+0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Whakareatia te \frac{4}{5} ki te 0, ka 0.
0+0+\frac{15}{30}\times 0\times 75=0\times 5
Whakareatia te 0 ki te 15, ka 0.
\frac{15}{30}\times 0\times 75=0\times 5
Tāpirihia te 0 ki te 0, ka 0.
\frac{1}{2}\times 0\times 75=0\times 5
Whakahekea te hautanga \frac{15}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 15.
0\times 75=0\times 5
Whakareatia te \frac{1}{2} ki te 0, ka 0.
0=0\times 5
Whakareatia te 0 ki te 75, ka 0.
0=0
Whakareatia te 0 ki te 5, ka 0.
\text{true}
Whakatauritea te 0 me te 0.
x\in \mathrm{R}
He pono tēnei mō tētahi x ahakoa.
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