Whakaoti i te -3x^2-24x-13=-13

$$- 3 x ^ { 2 } - 24 x - 13 = - 13$$

Whakaoti mō x

$$x=-8$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 13 ki ngā taha e rua.

$$-3x^{2}-24x-13+13=0$$

Tāpirihia te -13 ki te 13, ka 0.

$$-3x^{2}-24x=0$$

Tauwehea te x.

$$x\left(-3x-24\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -3x-24=0.

$$x=0 x=-8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-3x^{2}-24x-13=-13$$

Me tāpiri 13 ki ngā taha e rua o te whārite.

$$-3x^{2}-24x-13-\left(-13\right)=-13-\left(-13\right)$$

Mā te tango i te -13 i a ia ake anō ka toe ko te 0.

$$-3x^{2}-24x-13-\left(-13\right)=0$$

Tango -13 mai i -13.

$$-3x^{2}-24x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, -24 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te \left(-24\right)^{2}.

$$x=\frac{-\left(-24\right)±24}{2\left(-3\right)}$$

Ko te tauaro o -24 ko 24.

$$x=\frac{24±24}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{24±24}{-6}$$

Nā, me whakaoti te whārite x=\frac{24±24}{-6} ina he tāpiri te ±. Tāpiri 24 ki te 24.

$$x=\frac{48}{-6}$$

Whakawehe 48 ki te -6.

$$x=-8$$

Nā, me whakaoti te whārite x=\frac{24±24}{-6} ina he tango te ±. Tango 24 mai i 24.

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

Whakawehe 0 ki te -6.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-8 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$-3x^{2}-24x-13=-13$$

Me tāpiri 13 ki ngā taha e rua o te whārite.

$$-3x^{2}-24x-13-\left(-13\right)=-13-\left(-13\right)$$

Mā te tango i te -13 i a ia ake anō ka toe ko te 0.

$$-3x^{2}-24x=-13-\left(-13\right)$$

Tango -13 mai i -13.

$$-3x^{2}-24x=0$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}-24x}{-3}=\frac{0}{-3}$$

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

$$x^{2}+\left(-\frac{24}{-3}\right)x=\frac{0}{-3}$$

Whakawehe -24 ki te -3.

$$x^{2}+8x=\frac{0}{-3}$$

Whakawehe 0 ki te -3.

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

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

$$x^{2}+8x+4^{2}=4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=16$$

Tauwehea x^{2}+8x+16. 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}.

$$\left(x+4\right)^{2}=16$$

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

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x+4=4 x+4=-4$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=0 x=-8$$