Whakaoti i te 018+8x^2-18x=0

$$018 + 8 x ^ { 2 } - 18 x = 0$$

Whakaoti mō x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 0 ki te 18, ka 0.

$$0+8x^{2}-18x=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$8x^{2}-18x=0$$

Tauwehea te x.

$$x\left(8x-18\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 8x-18=0.

$$x=0 x=\frac{9}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 18, ka 0.

$$0+8x^{2}-18x=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$8x^{2}-18x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -18 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 8}$$

Tuhia te pūtakerua o te \left(-18\right)^{2}.

$$x=\frac{-\left(-18\right)±18}{2\times 8}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±18}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{18±18}{16}$$

Nā, me whakaoti te whārite x=\frac{18±18}{16} ina he tāpiri te ±. Tāpiri 18 ki te 18.

$$x=\frac{36}{16}$$

Whakahekea te hautanga \frac{36}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{9}{4}$$

Nā, me whakaoti te whārite x=\frac{18±18}{16} ina he tango te ±. Tango 18 mai i 18.

$$x=\frac{0}{16}$$

Whakawehe 0 ki te 16.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{9}{4} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 18, ka 0.

$$0+8x^{2}-18x=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$8x^{2}-18x=0$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}-18x}{8}=\frac{0}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$x^{2}+\left(-\frac{18}{8}\right)x=\frac{0}{8}$$

Whakahekea te hautanga \frac{-18}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{9}{4}x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x^{2}-\frac{9}{4}x=0$$

Whakawehea te -\frac{9}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{8}. Nā, tāpiria te pūrua o te -\frac{9}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{9}{4}x+\left(-\frac{9}{8}\right)^{2}=\left(-\frac{9}{8}\right)^{2}$$

Pūruatia -\frac{9}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{9}{4}x+\frac{81}{64}=\frac{81}{64}$$

Tauwehea x^{2}-\frac{9}{4}x+\frac{81}{64}. 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}.

$$\left(x-\frac{9}{8}\right)^{2}=\frac{81}{64}$$

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

$$\sqrt{\left(x-\frac{9}{8}\right)^{2}}=\sqrt{\frac{81}{64}}$$

Whakarūnātia.

$$x-\frac{9}{8}=\frac{9}{8} x-\frac{9}{8}=-\frac{9}{8}$$

Me tāpiri \frac{9}{8} ki ngā taha e rua o te whārite.

$$x=\frac{9}{4} x=0$$