Whakaoti i te 3x^2+11x-014=0

$$3 { x }^{ 2 } +11x-014=0$$

Whakaoti mō x

$$x = -\frac{11}{3} = -3\frac{2}{3} \approx -3.666666667$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 0 ki te 14, ka 0.

$$3x^{2}+11x-0=0$$

Whakaraupapatia anō ngā kīanga tau.

$$3x^{2}+11x=0$$

Tauwehea te x.

$$x\left(3x+11\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 3x+11=0.

$$x=0 x=-\frac{11}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 14, ka 0.

$$3x^{2}+11x-0=0$$

Whakaraupapatia anō ngā kīanga tau.

$$3x^{2}+11x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 11 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te 11^{2}.

$$x=\frac{-11±11}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-11±11}{6}$$

Nā, me whakaoti te whārite x=\frac{-11±11}{6} ina he tāpiri te ±. Tāpiri -11 ki te 11.

$$x=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-11±11}{6} ina he tango te ±. Tango 11 mai i -11.

$$x=-\frac{22}{6}$$

Whakahekea te hautanga \frac{-22}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{11}{3}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{11}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 14, ka 0.

$$3x^{2}+11x-0=0$$

Me tāpiri te 0 ki ngā taha e rua.

$$3x^{2}+11x=0+0$$

Tāpirihia te 0 ki te 0, ka 0.

$$3x^{2}+11x=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}+11x}{3}=\frac{0}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}+\frac{11}{3}x=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$x^{2}+\frac{11}{3}x=0$$

Whakawehea te \frac{11}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{11}{6}. Nā, tāpiria te pūrua o te \frac{11}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{11}{3}x+\left(\frac{11}{6}\right)^{2}=\left(\frac{11}{6}\right)^{2}$$

Pūruatia \frac{11}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{11}{3}x+\frac{121}{36}=\frac{121}{36}$$

Tauwehea te x^{2}+\frac{11}{3}x+\frac{121}{36}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{6}\right)^{2}=\frac{121}{36}$$

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

$$\sqrt{\left(x+\frac{11}{6}\right)^{2}}=\sqrt{\frac{121}{36}}$$

Whakarūnātia.

$$x+\frac{11}{6}=\frac{11}{6} x+\frac{11}{6}=-\frac{11}{6}$$

Me tango \frac{11}{6} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{11}{3}$$