Whakaoti i te 7+x/10=2/x+6

$$\frac{ 7+x }{ 10 } = \frac{ 2 }{ x+6 }$$

Whakaoti mō x

$$x=-11$$

$$x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10\left(x+6\right), arā, te tauraro pātahi he tino iti rawa te kitea o 10,x+6.

$$\left(x+6\right)\left(7+x\right)=10\times 2$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+6 ki te 7+x ka whakakotahi i ngā kupu rite.

$$13x+x^{2}+42=10\times 2$$

Whakareatia te 10 ki te 2, ka 20.

$$13x+x^{2}+42=20$$

Tangohia te 20 mai i ngā taha e rua.

$$13x+x^{2}+42-20=0$$

Tangohia te 20 i te 42, ka 22.

$$13x+x^{2}+22=0$$

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.

$$x^{2}+13x+22=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 13 mō b, me 22 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-13±\sqrt{13^{2}-4\times 22}}{2}$$

Pūrua 13.

$$x=\frac{-13±\sqrt{169-4\times 22}}{2}$$

Whakareatia -4 ki te 22.

$$x=\frac{-13±\sqrt{169-88}}{2}$$

Tāpiri 169 ki te -88.

$$x=\frac{-13±\sqrt{81}}{2}$$

Tuhia te pūtakerua o te 81.

$$x=\frac{-13±9}{2}$$

Nā, me whakaoti te whārite x=\frac{-13±9}{2} ina he tāpiri te ±. Tāpiri -13 ki te 9.

$$x=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-13±9}{2} ina he tango te ±. Tango 9 mai i -13.

$$x=-\frac{22}{2}$$

Whakawehe -22 ki te 2.

$$x=-11$$

Kua oti te whārite te whakatau.

$$x=-2 x=-11$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10\left(x+6\right), arā, te tauraro pātahi he tino iti rawa te kitea o 10,x+6.

$$\left(x+6\right)\left(7+x\right)=10\times 2$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+6 ki te 7+x ka whakakotahi i ngā kupu rite.

$$13x+x^{2}+42=10\times 2$$

Whakareatia te 10 ki te 2, ka 20.

$$13x+x^{2}+42=20$$

Tangohia te 42 mai i ngā taha e rua.

$$13x+x^{2}=20-42$$

Tangohia te 42 i te 20, ka -22.

$$13x+x^{2}=-22$$

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.

$$x^{2}+13x=-22$$

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.

$$x^{2}+13x+\left(\frac{13}{2}\right)^{2}=-22+\left(\frac{13}{2}\right)^{2}$$

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

$$x^{2}+13x+\frac{169}{4}=-22+\frac{169}{4}$$

Tāpiri -22 ki te \frac{169}{4}.

$$x^{2}+13x+\frac{169}{4}=\frac{81}{4}$$

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

$$\left(x+\frac{13}{2}\right)^{2}=\frac{81}{4}$$

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

$$\sqrt{\left(x+\frac{13}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Whakarūnātia.

$$x+\frac{13}{2}=\frac{9}{2} x+\frac{13}{2}=-\frac{9}{2}$$

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

$$x=-2 x=-11$$