Whakaoti i te 0=x^2+12x-18

$$0 = x ^ { 2 } + 12 x - 18$$

Whakaoti mō x

$$x=3\sqrt{6}-6\approx 1.348469228$$

$$x=-3\sqrt{6}-6\approx -13.348469228$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$x^{2}+12x-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-18\right)}}{2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-18\right)}}{2}$$

Whakareatia -4 ki te -18.

$$x=\frac{-12±\sqrt{144+72}}{2}$$

Tāpiri 144 ki te 72.

$$x=\frac{-12±\sqrt{216}}{2}$$

Tuhia te pūtakerua o te 216.

$$x=\frac{-12±6\sqrt{6}}{2}$$

Nā, me whakaoti te whārite x=\frac{-12±6\sqrt{6}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 6\sqrt{6}.

$$x=\frac{6\sqrt{6}-12}{2}$$

Whakawehe -12+6\sqrt{6} ki te 2.

$$x=3\sqrt{6}-6$$

Nā, me whakaoti te whārite x=\frac{-12±6\sqrt{6}}{2} ina he tango te ±. Tango 6\sqrt{6} mai i -12.

$$x=\frac{-6\sqrt{6}-12}{2}$$

Whakawehe -12-6\sqrt{6} ki te 2.

$$x=-3\sqrt{6}-6$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{6}-6 x=-3\sqrt{6}-6$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$x^{2}+12x-18=0$$

Me tāpiri te 18 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}+12x=18$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+12x+6^{2}=18+6^{2}$$

Pūrua 6.

$$x^{2}+12x+36=18+36$$

Tāpiri 18 ki te 36.

$$x^{2}+12x+36=54$$

Tauwehea x^{2}+12x+36. 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}.

$$\left(x+6\right)^{2}=54$$

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

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{54}$$

Whakarūnātia.

$$x+6=3\sqrt{6} x+6=-3\sqrt{6}$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=3\sqrt{6}-6 x=-3\sqrt{6}-6$$