Whakaoti i te 34-x=288/x

$$34 - x = \frac { 288 } { x }$$

Whakaoti mō x

$$x=16$$

$$x=18$$

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.

$$x\times 34-xx=288$$

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

$$x\times 34-x^{2}=288$$

Tangohia te 288 mai i ngā taha e rua.

$$x\times 34-x^{2}-288=0$$

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.

$$-x^{2}+34x-288=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 34 mō b, me -288 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-34±\sqrt{34^{2}-4\left(-1\right)\left(-288\right)}}{2\left(-1\right)}$$

Pūrua 34.

$$x=\frac{-34±\sqrt{1156-4\left(-1\right)\left(-288\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-34±\sqrt{1156+4\left(-288\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -288.

$$x=\frac{-34±\sqrt{1156-1152}}{2\left(-1\right)}$$

Tāpiri 1156 ki te -1152.

$$x=\frac{-34±\sqrt{4}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{-34±2}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-34±2}{-2}$$

Nā, me whakaoti te whārite x=\frac{-34±2}{-2} ina he tāpiri te ±. Tāpiri -34 ki te 2.

$$x=-\frac{32}{-2}$$

Whakawehe -32 ki te -2.

$$x=16$$

Nā, me whakaoti te whārite x=\frac{-34±2}{-2} ina he tango te ±. Tango 2 mai i -34.

$$x=-\frac{36}{-2}$$

Whakawehe -36 ki te -2.

$$x=18$$

Kua oti te whārite te whakatau.

$$x=16 x=18$$

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.

$$x\times 34-xx=288$$

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

$$x\times 34-x^{2}=288$$

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.

$$-x^{2}+34x=288$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+34x}{-1}=\frac{288}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{34}{-1}x=\frac{288}{-1}$$

Whakawehe 34 ki te -1.

$$x^{2}-34x=\frac{288}{-1}$$

Whakawehe 288 ki te -1.

$$x^{2}-34x=-288$$

Whakawehea te -34, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -17. Nā, tāpiria te pūrua o te -17 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-34x+\left(-17\right)^{2}=-288+\left(-17\right)^{2}$$

Pūrua -17.

$$x^{2}-34x+289=-288+289$$

Tāpiri -288 ki te 289.

$$x^{2}-34x+289=1$$

Tauwehea x^{2}-34x+289. 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}.

$$\left(x-17\right)^{2}=1$$

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

$$\sqrt{\left(x-17\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$x-17=1 x-17=-1$$

Me tāpiri 17 ki ngā taha e rua o te whārite.

$$x=18 x=16$$