Whakaoti i te x+84=160divx

$$x+84=160 \div x$$

Whakaoti mō x

$$x=2\sqrt{481}-42\approx 1.863424399$$

$$x=-2\sqrt{481}-42\approx -85.863424399$$

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.

$$xx+x\times 84=160$$

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

$$x^{2}+x\times 84=160$$

Tangohia te 160 mai i ngā taha e rua.

$$x^{2}+x\times 84-160=0$$

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.

$$x^{2}+84x-160=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 84 mō b, me -160 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-84±\sqrt{84^{2}-4\left(-160\right)}}{2}$$

Pūrua 84.

$$x=\frac{-84±\sqrt{7056-4\left(-160\right)}}{2}$$

Whakareatia -4 ki te -160.

$$x=\frac{-84±\sqrt{7056+640}}{2}$$

Tāpiri 7056 ki te 640.

$$x=\frac{-84±\sqrt{7696}}{2}$$

Tuhia te pūtakerua o te 7696.

$$x=\frac{-84±4\sqrt{481}}{2}$$

Nā, me whakaoti te whārite x=\frac{-84±4\sqrt{481}}{2} ina he tāpiri te ±. Tāpiri -84 ki te 4\sqrt{481}.

$$x=\frac{4\sqrt{481}-84}{2}$$

Whakawehe -84+4\sqrt{481} ki te 2.

$$x=2\sqrt{481}-42$$

Nā, me whakaoti te whārite x=\frac{-84±4\sqrt{481}}{2} ina he tango te ±. Tango 4\sqrt{481} mai i -84.

$$x=\frac{-4\sqrt{481}-84}{2}$$

Whakawehe -84-4\sqrt{481} ki te 2.

$$x=-2\sqrt{481}-42$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{481}-42 x=-2\sqrt{481}-42$$

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.

$$xx+x\times 84=160$$

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

$$x^{2}+x\times 84=160$$

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.

$$x^{2}+84x=160$$

Whakawehea te 84, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 42. Nā, tāpiria te pūrua o te 42 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+84x+42^{2}=160+42^{2}$$

Pūrua 42.

$$x^{2}+84x+1764=160+1764$$

Tāpiri 160 ki te 1764.

$$x^{2}+84x+1764=1924$$

Tauwehea x^{2}+84x+1764. 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}.

$$\left(x+42\right)^{2}=1924$$

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

$$\sqrt{\left(x+42\right)^{2}}=\sqrt{1924}$$

Whakarūnātia.

$$x+42=2\sqrt{481} x+42=-2\sqrt{481}$$

Me tango 42 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{481}-42 x=-2\sqrt{481}-42$$