Whakaoti i te 10(10+8)=x(3+x)

$$10 ( 10 + 8 ) = x ( 3 + x )$$

Whakaoti mō x

$$x=-15$$

$$x=12$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 10 ki te 8, ka 18.

$$10\times 18=x\left(3+x\right)$$

Whakareatia te 10 ki te 18, ka 180.

$$180=x\left(3+x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 3+x.

$$180=3x+x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3x+x^{2}=180$$

Tangohia te 180 mai i ngā taha e rua.

$$3x+x^{2}-180=0$$

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.

$$x^{2}+3x-180=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 3 mō b, me -180 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-180\right)}}{2}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-180\right)}}{2}$$

Whakareatia -4 ki te -180.

$$x=\frac{-3±\sqrt{9+720}}{2}$$

Tāpiri 9 ki te 720.

$$x=\frac{-3±\sqrt{729}}{2}$$

Tuhia te pūtakerua o te 729.

$$x=\frac{-3±27}{2}$$

Nā, me whakaoti te whārite x=\frac{-3±27}{2} ina he tāpiri te ±. Tāpiri -3 ki te 27.

$$x=\frac{24}{2}$$

Whakawehe 24 ki te 2.

$$x=12$$

Nā, me whakaoti te whārite x=\frac{-3±27}{2} ina he tango te ±. Tango 27 mai i -3.

$$x=-\frac{30}{2}$$

Whakawehe -30 ki te 2.

$$x=-15$$

Kua oti te whārite te whakatau.

$$x=12 x=-15$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpirihia te 10 ki te 8, ka 18.

$$10\times 18=x\left(3+x\right)$$

Whakareatia te 10 ki te 18, ka 180.

$$180=x\left(3+x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 3+x.

$$180=3x+x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3x+x^{2}=180$$

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.

$$x^{2}+3x=180$$

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

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=180+\left(\frac{3}{2}\right)^{2}$$

Pūruatia \frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+3x+\frac{9}{4}=180+\frac{9}{4}$$

Tāpiri 180 ki te \frac{9}{4}.

$$x^{2}+3x+\frac{9}{4}=\frac{729}{4}$$

Tauwehea te x^{2}+3x+\frac{9}{4}. 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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{729}{4}$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{729}{4}}$$

Whakarūnātia.

$$x+\frac{3}{2}=\frac{27}{2} x+\frac{3}{2}=-\frac{27}{2}$$

Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.

$$x=12 x=-15$$