Whakaoti i te -270x=30x^2

$$- 270 x = 30 x ^ { 2 }$$

Whakaoti mō x

$$x=-9$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 30x^{2} mai i ngā taha e rua.

$$-270x-30x^{2}=0$$

Tauwehea te x.

$$x\left(-270-30x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -270-30x=0.

$$x=0 x=-9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 30x^{2} mai i ngā taha e rua.

$$-270x-30x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-30x^{2}-270x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -30 mō a, -270 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-270\right)±\sqrt{\left(-270\right)^{2}}}{2\left(-30\right)}$$

Tuhia te pūtakerua o te \left(-270\right)^{2}.

$$x=\frac{-\left(-270\right)±270}{2\left(-30\right)}$$

Ko te tauaro o -270 ko 270.

$$x=\frac{270±270}{2\left(-30\right)}$$

Whakareatia 2 ki te -30.

$$x=\frac{270±270}{-60}$$

Nā, me whakaoti te whārite x=\frac{270±270}{-60} ina he tāpiri te ±. Tāpiri 270 ki te 270.

$$x=\frac{540}{-60}$$

Whakawehe 540 ki te -60.

$$x=-9$$

Nā, me whakaoti te whārite x=\frac{270±270}{-60} ina he tango te ±. Tango 270 mai i 270.

$$x=\frac{0}{-60}$$

Whakawehe 0 ki te -60.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-9 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 30x^{2} mai i ngā taha e rua.

$$-270x-30x^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-30x^{2}-270x=0$$

Whakawehea ngā taha e rua ki te -30.

$$\frac{-30x^{2}-270x}{-30}=\frac{0}{-30}$$

Mā te whakawehe ki te -30 ka wetekia te whakareanga ki te -30.

$$x^{2}+\left(-\frac{270}{-30}\right)x=\frac{0}{-30}$$

Whakawehe -270 ki te -30.

$$x^{2}+9x=\frac{0}{-30}$$

Whakawehe 0 ki te -30.

$$x^{2}+9x=0$$

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

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

Pūruatia \frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

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

$$\left(x+\frac{9}{2}\right)^{2}=\frac{81}{4}$$

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

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Whakarūnātia.

$$x+\frac{9}{2}=\frac{9}{2} x+\frac{9}{2}=-\frac{9}{2}$$

Me tango \frac{9}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-9$$