Whakaoti i te x=7/5x-3

$$x = \frac { 7 } { 5 x - 3 }$$

Whakaoti mō x

$$x = \frac{\sqrt{149} + 3}{10} \approx 1.520655562$$

$$x=\frac{3-\sqrt{149}}{10}\approx -0.920655562$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{7}{5x-3} mai i ngā taha e rua.

$$x-\frac{7}{5x-3}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{5x-3}{5x-3}.

$$\frac{x\left(5x-3\right)}{5x-3}-\frac{7}{5x-3}=0$$

Tā te mea he rite te tauraro o \frac{x\left(5x-3\right)}{5x-3} me \frac{7}{5x-3}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(5x-3\right)-7}{5x-3}=0$$

Mahia ngā whakarea i roto o x\left(5x-3\right)-7.

$$\frac{5x^{2}-3x-7}{5x-3}=0$$

Tē taea kia ōrite te tāupe x ki \frac{3}{5} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 5x-3.

$$5x^{2}-3x-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -3 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 5\left(-7\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-3\right)±\sqrt{9-20\left(-7\right)}}{2\times 5}$$

Whakareatia -20 ki te -7.

$$x=\frac{-\left(-3\right)±\sqrt{9+140}}{2\times 5}$$

Tāpiri 9 ki te 140.

$$x=\frac{-\left(-3\right)±\sqrt{149}}{2\times 5}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±\sqrt{149}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{3±\sqrt{149}}{10}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{149}}{10} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{149}.

$$x=\frac{\sqrt{149}+3}{10}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{149}}{10} ina he tango te ±. Tango \sqrt{149} mai i 3.

$$x=\frac{3-\sqrt{149}}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{149}+3}{10} x=\frac{3-\sqrt{149}}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te \frac{7}{5x-3} mai i ngā taha e rua.

$$x-\frac{7}{5x-3}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{5x-3}{5x-3}.

$$\frac{x\left(5x-3\right)}{5x-3}-\frac{7}{5x-3}=0$$

Tā te mea he rite te tauraro o \frac{x\left(5x-3\right)}{5x-3} me \frac{7}{5x-3}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(5x-3\right)-7}{5x-3}=0$$

Mahia ngā whakarea i roto o x\left(5x-3\right)-7.

$$\frac{5x^{2}-3x-7}{5x-3}=0$$

Tē taea kia ōrite te tāupe x ki \frac{3}{5} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 5x-3.

$$5x^{2}-3x-7=0$$

Me tāpiri te 7 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$5x^{2}-3x=7$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-3x}{5}=\frac{7}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}-\frac{3}{5}x=\frac{7}{5}$$

Whakawehea te -\frac{3}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{10}. Nā, tāpiria te pūrua o te -\frac{3}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{3}{5}x+\left(-\frac{3}{10}\right)^{2}=\frac{7}{5}+\left(-\frac{3}{10}\right)^{2}$$

Pūruatia -\frac{3}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{5}x+\frac{9}{100}=\frac{7}{5}+\frac{9}{100}$$

Tāpiri \frac{7}{5} ki te \frac{9}{100} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{3}{5}x+\frac{9}{100}=\frac{149}{100}$$

Tauwehea x^{2}-\frac{3}{5}x+\frac{9}{100}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{10}\right)^{2}=\frac{149}{100}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{3}{10}\right)^{2}}=\sqrt{\frac{149}{100}}$$

Whakarūnātia.

$$x-\frac{3}{10}=\frac{\sqrt{149}}{10} x-\frac{3}{10}=-\frac{\sqrt{149}}{10}$$

Me tāpiri \frac{3}{10} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{149}+3}{10} x=\frac{3-\sqrt{149}}{10}$$