Whakaoti i te 5x^2=8x-16/5

$$5 x ^ { 2 } = 8 x - \frac { 16 } { 5 }$$

Whakaoti mō x

$$x=\frac{4}{5}=0.8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 8x mai i ngā taha e rua.

$$5x^{2}-8x=-\frac{16}{5}$$

Me tāpiri te \frac{16}{5} ki ngā taha e rua.

$$5x^{2}-8x+\frac{16}{5}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -8 mō b, me \frac{16}{5} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 5\times \frac{16}{5}}}{2\times 5}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 5\times \frac{16}{5}}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-8\right)±\sqrt{64-20\times \frac{16}{5}}}{2\times 5}$$

Whakareatia -20 ki te \frac{16}{5}.

$$x=\frac{-\left(-8\right)±\sqrt{64-64}}{2\times 5}$$

Tāpiri 64 ki te -64.

$$x=\frac{-\left(-8\right)±\sqrt{0}}{2\times 5}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{-8}{2\times 5}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{8}{10}$$

Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{4}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 8x mai i ngā taha e rua.

$$5x^{2}-8x=-\frac{16}{5}$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-8x}{5}=-\frac{\frac{16}{5}}{5}$$

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

$$x^{2}-\frac{8}{5}x=-\frac{\frac{16}{5}}{5}$$

Whakawehe -\frac{16}{5} ki te 5.

$$x^{2}-\frac{8}{5}x=-\frac{16}{25}$$

Whakawehea te -\frac{8}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{4}{5}. Nā, tāpiria te pūrua o te -\frac{4}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{8}{5}x+\left(-\frac{4}{5}\right)^{2}=-\frac{16}{25}+\left(-\frac{4}{5}\right)^{2}$$

Pūruatia -\frac{4}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{8}{5}x+\frac{16}{25}=\frac{-16+16}{25}$$

Tāpiri -\frac{16}{25} ki te \frac{16}{25} 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.

$$x^{2}-\frac{8}{5}x+\frac{16}{25}=0$$

Tauwehea x^{2}-\frac{8}{5}x+\frac{16}{25}. 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}.

$$\left(x-\frac{4}{5}\right)^{2}=0$$

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

$$\sqrt{\left(x-\frac{4}{5}\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x-\frac{4}{5}=0 x-\frac{4}{5}=0$$

Me tāpiri \frac{4}{5} ki ngā taha e rua o te whārite.

$$x=\frac{4}{5} x=\frac{4}{5}$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=\frac{4}{5}$$