Whakaoti i te n^2+3n-12=6

$$n ^ { 2 } + 3 n - 12 = 6$$

Whakaoti mō n

$$n=-6$$

$$n=3$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 6 mai i ngā taha e rua.

$$n^{2}+3n-12-6=0$$

Tangohia te 6 i te -12, ka -18.

$$n^{2}+3n-18=0$$

Hei whakaoti i te whārite, whakatauwehea te n^{2}+3n-18 mā te whakamahi i te tātai n^{2}+\left(a+b\right)n+ab=\left(n+a\right)\left(n+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=-18$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -18.

$$-1,18 -2,9 -3,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+18=17 -2+9=7 -3+6=3$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=-3 b=6$$

Me tuhi anō te kīanga whakatauwehe \left(n+a\right)\left(n+b\right) mā ngā uara i tātaihia.

$$\left(n-3\right)\left(n+6\right)$$

Hei kimi otinga whārite, me whakaoti te n-3=0 me te n+6=0.

$$n=3 n=-6$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 6 mai i ngā taha e rua.

$$n^{2}+3n-12-6=0$$

Tangohia te 6 i te -12, ka -18.

$$n^{2}+3n-18=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei n^{2}+an+bn-18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=1\left(-18\right)=-18$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -18.

$$-1,18 -2,9 -3,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+18=17 -2+9=7 -3+6=3$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=-3 b=6$$

Tuhia anō te n^{2}+3n-18 hei \left(n^{2}-3n\right)+\left(6n-18\right).

$$\left(n^{2}-3n\right)+\left(6n-18\right)$$

Tauwehea te n i te tuatahi me te 6 i te rōpū tuarua.

$$n\left(n-3\right)+6\left(n-3\right)$$

Whakatauwehea atu te kīanga pātahi n-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(n-3\right)\left(n+6\right)$$

Hei kimi otinga whārite, me whakaoti te n-3=0 me te n+6=0.

$$n=3 n=-6$$

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.

$$n^{2}+3n-12=6$$

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

$$n^{2}+3n-12-6=6-6$$

Mā te tango i te 6 i a ia ake anō ka toe ko te 0.

$$n^{2}+3n-12-6=0$$

Tango 6 mai i -12.

$$n^{2}+3n-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 3 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-3±\sqrt{3^{2}-4\left(-18\right)}}{2}$$

Pūrua 3.

$$n=\frac{-3±\sqrt{9-4\left(-18\right)}}{2}$$

Whakareatia -4 ki te -18.

$$n=\frac{-3±\sqrt{9+72}}{2}$$

Tāpiri 9 ki te 72.

$$n=\frac{-3±\sqrt{81}}{2}$$

Tuhia te pūtakerua o te 81.

$$n=\frac{-3±9}{2}$$

Nā, me whakaoti te whārite n=\frac{-3±9}{2} ina he tāpiri te ±. Tāpiri -3 ki te 9.

$$n=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$n=3$$

Nā, me whakaoti te whārite n=\frac{-3±9}{2} ina he tango te ±. Tango 9 mai i -3.

$$n=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$n=-6$$

Kua oti te whārite te whakatau.

$$n=3 n=-6$$

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.

$$n^{2}+3n-12=6$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$n^{2}+3n-12-\left(-12\right)=6-\left(-12\right)$$

Mā te tango i te -12 i a ia ake anō ka toe ko te 0.

$$n^{2}+3n=6-\left(-12\right)$$

Tango -12 mai i 6.

$$n^{2}+3n=18$$

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.

$$n^{2}+3n+\left(\frac{3}{2}\right)^{2}=18+\left(\frac{3}{2}\right)^{2}$$

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

$$n^{2}+3n+\frac{9}{4}=18+\frac{9}{4}$$

Tāpiri 18 ki te \frac{9}{4}.

$$n^{2}+3n+\frac{9}{4}=\frac{81}{4}$$

Tauwehea n^{2}+3n+\frac{9}{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}.

$$\left(n+\frac{3}{2}\right)^{2}=\frac{81}{4}$$

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

$$\sqrt{\left(n+\frac{3}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Whakarūnātia.

$$n+\frac{3}{2}=\frac{9}{2} n+\frac{3}{2}=-\frac{9}{2}$$

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

$$n=3 n=-6$$