Whakaoti i te 6x^2=x+28

$$6 x ^ { 2 } = x + 28$$

Whakaoti mō x

$$x = \frac{\sqrt{673} + 1}{12} \approx 2.245186962$$

$$x=\frac{1-\sqrt{673}}{12}\approx -2.078520295$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x mai i ngā taha e rua.

$$6x^{2}-x=28$$

Tangohia te 28 mai i ngā taha e rua.

$$6x^{2}-x-28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -1 mō b, me -28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 6\left(-28\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-1\right)±\sqrt{1-24\left(-28\right)}}{2\times 6}$$

Whakareatia -24 ki te -28.

$$x=\frac{-\left(-1\right)±\sqrt{1+672}}{2\times 6}$$

Tāpiri 1 ki te 672.

$$x=\frac{-\left(-1\right)±\sqrt{673}}{2\times 6}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{673}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{1±\sqrt{673}}{12}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{673}}{12} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{673}.

$$x=\frac{\sqrt{673}+1}{12}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{673}}{12} ina he tango te ±. Tango \sqrt{673} mai i 1.

$$x=\frac{1-\sqrt{673}}{12}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{673}+1}{12} x=\frac{1-\sqrt{673}}{12}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x mai i ngā taha e rua.

$$6x^{2}-x=28$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-x}{6}=\frac{28}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}-\frac{1}{6}x=\frac{28}{6}$$

Whakahekea te hautanga \frac{28}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{1}{6}x=\frac{14}{3}$$

Whakawehea te -\frac{1}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{12}. Nā, tāpiria te pūrua o te -\frac{1}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{6}x+\left(-\frac{1}{12}\right)^{2}=\frac{14}{3}+\left(-\frac{1}{12}\right)^{2}$$

Pūruatia -\frac{1}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{14}{3}+\frac{1}{144}$$

Tāpiri \frac{14}{3} ki te \frac{1}{144} 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.

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{673}{144}$$

Tauwehea x^{2}-\frac{1}{6}x+\frac{1}{144}. 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}.

$$\left(x-\frac{1}{12}\right)^{2}=\frac{673}{144}$$

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

$$\sqrt{\left(x-\frac{1}{12}\right)^{2}}=\sqrt{\frac{673}{144}}$$

Whakarūnātia.

$$x-\frac{1}{12}=\frac{\sqrt{673}}{12} x-\frac{1}{12}=-\frac{\sqrt{673}}{12}$$

Me tāpiri \frac{1}{12} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{673}+1}{12} x=\frac{1-\sqrt{673}}{12}$$