Whakaoti i te (15quad3x^2=27x

$$( 15 \quad 3 x ^ { 2 } = 27 x$$

Whakaoti mō x

$$x=\frac{3}{17}\approx 0.176470588$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 27x mai i ngā taha e rua.

$$153x^{2}-27x=0$$

Tauwehea te x.

$$x\left(153x-27\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 153x-27=0.

$$x=0 x=\frac{3}{17}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 27x mai i ngā taha e rua.

$$153x^{2}-27x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 153 mō a, -27 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}}}{2\times 153}$$

Tuhia te pūtakerua o te \left(-27\right)^{2}.

$$x=\frac{-\left(-27\right)±27}{2\times 153}$$

Ko te tauaro o -27 ko 27.

$$x=\frac{27±27}{2\times 153}$$

Whakareatia 2 ki te 153.

$$x=\frac{27±27}{306}$$

Nā, me whakaoti te whārite x=\frac{27±27}{306} ina he tāpiri te ±. Tāpiri 27 ki te 27.

$$x=\frac{54}{306}$$

Whakahekea te hautanga \frac{54}{306} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$x=\frac{3}{17}$$

Nā, me whakaoti te whārite x=\frac{27±27}{306} ina he tango te ±. Tango 27 mai i 27.

$$x=\frac{0}{306}$$

Whakawehe 0 ki te 306.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{17} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 27x mai i ngā taha e rua.

$$153x^{2}-27x=0$$

Whakawehea ngā taha e rua ki te 153.

$$\frac{153x^{2}-27x}{153}=\frac{0}{153}$$

Mā te whakawehe ki te 153 ka wetekia te whakareanga ki te 153.

$$x^{2}+\left(-\frac{27}{153}\right)x=\frac{0}{153}$$

Whakahekea te hautanga \frac{-27}{153} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$x^{2}-\frac{3}{17}x=\frac{0}{153}$$

Whakawehe 0 ki te 153.

$$x^{2}-\frac{3}{17}x=0$$

Whakawehea te -\frac{3}{17}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{34}. Nā, tāpiria te pūrua o te -\frac{3}{34} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{3}{17}x+\left(-\frac{3}{34}\right)^{2}=\left(-\frac{3}{34}\right)^{2}$$

Pūruatia -\frac{3}{34} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{17}x+\frac{9}{1156}=\frac{9}{1156}$$

Tauwehea x^{2}-\frac{3}{17}x+\frac{9}{1156}. 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}.

$$\left(x-\frac{3}{34}\right)^{2}=\frac{9}{1156}$$

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

$$\sqrt{\left(x-\frac{3}{34}\right)^{2}}=\sqrt{\frac{9}{1156}}$$

Whakarūnātia.

$$x-\frac{3}{34}=\frac{3}{34} x-\frac{3}{34}=-\frac{3}{34}$$

Me tāpiri \frac{3}{34} ki ngā taha e rua o te whārite.

$$x=\frac{3}{17} x=0$$