Whakaoti i te x^2=18+3x

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

Whakaoti mō x

$$x=-3$$

$$x=6$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 18 mai i ngā taha e rua.

$$x^{2}-18=3x$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-18-3x=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$x^{2}-3x-18=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-3x-18 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+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 tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. 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.

$$a=-6 b=3$$

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

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

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

$$x=6 x=-3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 18 mai i ngā taha e rua.

$$x^{2}-18=3x$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-18-3x=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$x^{2}-3x-18=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-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 tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. 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.

$$a=-6 b=3$$

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

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

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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

$$x=6 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 18 mai i ngā taha e rua.

$$x^{2}-18=3x$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-18-3x=0$$

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.

$$x^{2}-3x-18=0$$

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}.

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

Pūrua -3.

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

Whakareatia -4 ki te -18.

$$x=\frac{-\left(-3\right)±\sqrt{9+72}}{2}$$

Tāpiri 9 ki te 72.

$$x=\frac{-\left(-3\right)±\sqrt{81}}{2}$$

Tuhia te pūtakerua o te 81.

$$x=\frac{-\left(-3\right)±9}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±9}{2}$$

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

$$x=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$x=6$$

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

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

Whakawehe -6 ki te 2.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=6 x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-3x=18$$

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.

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

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

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

Tāpiri 18 ki te \frac{9}{4}.

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

Tauwehea x^{2}-3x+\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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{81}{4}$$

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

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

Whakarūnātia.

$$x-\frac{3}{2}=\frac{9}{2} x-\frac{3}{2}=-\frac{9}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=6 x=-3$$