Whakaoti i te x+36/x=-13

$$x + \frac { 36 } { x } = - 13$$

Whakaoti mō x

$$x=-9$$

$$x=-4$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$xx+36=-13x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+36=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$x^{2}+36+13x=0$$

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

$$x^{2}+13x+36=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+13x+36 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.

$$a+b=13 ab=36$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 36.

$$1,36 2,18 3,12 4,9 6,6$$

Tātaihia te tapeke mō ia takirua.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=4 b=9$$

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

$$\left(x+4\right)\left(x+9\right)$$

Hei kimi otinga whārite, me whakaoti te x+4=0 me te x+9=0.

$$x=-4 x=-9$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$xx+36=-13x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+36=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$x^{2}+36+13x=0$$

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

$$x^{2}+13x+36=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=13 ab=1\times 36=36$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 36.

$$1,36 2,18 3,12 4,9 6,6$$

Tātaihia te tapeke mō ia takirua.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=4 b=9$$

Tuhia anō te x^{2}+13x+36 hei \left(x^{2}+4x\right)+\left(9x+36\right).

$$\left(x^{2}+4x\right)+\left(9x+36\right)$$

Tauwehea te x i te tuatahi me te 9 i te rōpū tuarua.

$$x\left(x+4\right)+9\left(x+4\right)$$

Whakatauwehea atu te kīanga pātahi x+4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+4\right)\left(x+9\right)$$

Hei kimi otinga whārite, me whakaoti te x+4=0 me te x+9=0.

$$x=-4 x=-9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$xx+36=-13x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+36=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$x^{2}+36+13x=0$$

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.

$$x^{2}+13x+36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 13 mō b, me 36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-13±\sqrt{13^{2}-4\times 36}}{2}$$

Pūrua 13.

$$x=\frac{-13±\sqrt{169-4\times 36}}{2}$$

Whakareatia -4 ki te 36.

$$x=\frac{-13±\sqrt{169-144}}{2}$$

Tāpiri 169 ki te -144.

$$x=\frac{-13±\sqrt{25}}{2}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-13±5}{2}$$

Nā, me whakaoti te whārite x=\frac{-13±5}{2} ina he tāpiri te ±. Tāpiri -13 ki te 5.

$$x=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$x=-4$$

Nā, me whakaoti te whārite x=\frac{-13±5}{2} ina he tango te ±. Tango 5 mai i -13.

$$x=-\frac{18}{2}$$

Whakawehe -18 ki te 2.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=-4 x=-9$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$xx+36=-13x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+36=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$x^{2}+36+13x=0$$

Tangohia te 36 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+13x=-36$$

Whakawehea te 13, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{13}{2}. Nā, tāpiria te pūrua o te \frac{13}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+13x+\left(\frac{13}{2}\right)^{2}=-36+\left(\frac{13}{2}\right)^{2}$$

Pūruatia \frac{13}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+13x+\frac{169}{4}=-36+\frac{169}{4}$$

Tāpiri -36 ki te \frac{169}{4}.

$$x^{2}+13x+\frac{169}{4}=\frac{25}{4}$$

Tauwehea te x^{2}+13x+\frac{169}{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}.

$$\left(x+\frac{13}{2}\right)^{2}=\frac{25}{4}$$

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

$$\sqrt{\left(x+\frac{13}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Whakarūnātia.

$$x+\frac{13}{2}=\frac{5}{2} x+\frac{13}{2}=-\frac{5}{2}$$

Me tango \frac{13}{2} mai i ngā taha e rua o te whārite.

$$x=-4 x=-9$$