Whakaoti i te (1215-x)*30000+30000=36790/x

$$( 1215 - x ) \times 30000 + 30000 = \frac { 36790 } { x }$$

Whakaoti mō x

$$x=\frac{\sqrt{33269649630}}{300}+608\approx 1215.998991501$$

$$x=-\frac{\sqrt{33269649630}}{300}+608\approx 0.001008499$$

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.

$$\left(1215-x\right)\times 30000x+x\times 30000=36790$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1215-x ki te 30000.

$$\left(36450000-30000x\right)x+x\times 30000=36790$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36450000-30000x ki te x.

$$36450000x-30000x^{2}+x\times 30000=36790$$

Pahekotia te 36450000x me x\times 30000, ka 36480000x.

$$36480000x-30000x^{2}=36790$$

Tangohia te 36790 mai i ngā taha e rua.

$$36480000x-30000x^{2}-36790=0$$

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.

$$-30000x^{2}[phone]x-36790=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -30000 mō a, 36480000 mō b, me -36790 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-36480000±\sqrt{36480000^{2}-4\left(-30000\right)\left(-36790\right)}}{2\left(-30000\right)}$$

Pūrua 36480000.

$$x=\frac{-36480000±\sqrt{1330790400000000-4\left(-30000\right)\left(-36790\right)}}{2\left(-30000\right)}$$

Whakareatia -4 ki te -30000.

$$x=\frac{-36480000±\sqrt{1330790400000000+120000\left(-36790\right)}}{2\left(-30000\right)}$$

Whakareatia 120000 ki te -36790.

$$x=\frac{-36480000±\sqrt{1330790400000000-4414800000}}{2\left(-30000\right)}$$

Tāpiri 1330790400000000 ki te -4414800000.

$$x=\frac{-36480000±\sqrt{1330785985200000}}{2\left(-30000\right)}$$

Tuhia te pūtakerua o te 1330785985200000.

$$x=\frac{-36480000±200\sqrt{33269649630}}{2\left(-30000\right)}$$

Whakareatia 2 ki te -30000.

$$x=\frac{-36480000±200\sqrt{33269649630}}{-60000}$$

Nā, me whakaoti te whārite x=\frac{-36480000±200\sqrt{33269649630}}{-60000} ina he tāpiri te ±. Tāpiri -36480000 ki te 200\sqrt{33269649630}.

$$x=\frac{200\sqrt{33269649630}-36480000}{-60000}$$

Whakawehe -36480000+200\sqrt{33269649630} ki te -60000.

$$x=-\frac{\sqrt{33269649630}}{300}+608$$

Nā, me whakaoti te whārite x=\frac{-36480000±200\sqrt{33269649630}}{-60000} ina he tango te ±. Tango 200\sqrt{33269649630} mai i -36480000.

$$x=\frac{-200\sqrt{33269649630}-36480000}{-60000}$$

Whakawehe -36480000-200\sqrt{33269649630} ki te -60000.

$$x=\frac{\sqrt{33269649630}}{300}+608$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{33269649630}}{300}+608 x=\frac{\sqrt{33269649630}}{300}+608$$

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.

$$\left(1215-x\right)\times 30000x+x\times 30000=36790$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1215-x ki te 30000.

$$\left(36450000-30000x\right)x+x\times 30000=36790$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36450000-30000x ki te x.

$$36450000x-30000x^{2}+x\times 30000=36790$$

Pahekotia te 36450000x me x\times 30000, ka 36480000x.

$$36480000x-30000x^{2}=36790$$

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.

$$-30000x^{2}[phone]x=36790$$

Whakawehea ngā taha e rua ki te -30000.

$$\frac{-30000x^{2}[phone]x}{-30000}=\frac{36790}{-30000}$$

Mā te whakawehe ki te -30000 ka wetekia te whakareanga ki te -30000.

$$x^{2}+\frac{36480000}{-30000}x=\frac{36790}{-30000}$$

Whakawehe 36480000 ki te -30000.

$$x^{2}-1216x=\frac{36790}{-30000}$$

Whakahekea te hautanga \frac{36790}{-30000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x^{2}-1216x=-\frac{3679}{3000}$$

Whakawehea te -1216, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -608. Nā, tāpiria te pūrua o te -608 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-1216x+\left(-608\right)^{2}=-\frac{3679}{3000}+\left(-608\right)^{2}$$

Pūrua -608.

$$x^{2}-1216x+369664=-\frac{3679}{3000}+369664$$

Tāpiri -\frac{3679}{3000} ki te 369664.

$$x^{2}-1216x+369664=\frac{1108988321}{3000}$$

Tauwehea x^{2}-1216x+369664. 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}.

$$\left(x-608\right)^{2}=\frac{1108988321}{3000}$$

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

$$\sqrt{\left(x-608\right)^{2}}=\sqrt{\frac{1108988321}{3000}}$$

Whakarūnātia.

$$x-608=\frac{\sqrt{33269649630}}{300} x-608=-\frac{\sqrt{33269649630}}{300}$$

Me tāpiri 608 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{33269649630}}{300}+608 x=-\frac{\sqrt{33269649630}}{300}+608$$