Whakaoti i te 2x/210-x=210-x/2x

$$\frac { 2 x } { 210 - x } = \frac { 210 - x } { 2 x }$$

Whakaoti mō x

$$x=-210$$

$$x=70$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,210 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-210\right), arā, te tauraro pātahi he tino iti rawa te kitea o 210-x,2x.

$$-2x\times 2x=\left(x-210\right)\left(210-x\right)$$

Whakareatia te -2 ki te 2, ka -4.

$$-4xx=\left(x-210\right)\left(210-x\right)$$

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

$$-4x^{2}=\left(x-210\right)\left(210-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-210 ki te 210-x ka whakakotahi i ngā kupu rite.

$$-4x^{2}=420x-x^{2}-44100$$

Tangohia te 420x mai i ngā taha e rua.

$$-4x^{2}-420x=-x^{2}-44100$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$-4x^{2}-420x+x^{2}=-44100$$

Pahekotia te -4x^{2} me x^{2}, ka -3x^{2}.

$$-3x^{2}-420x=-44100$$

Me tāpiri te 44100 ki ngā taha e rua.

$$-3x^{2}-420x+44100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, -420 mō b, me 44100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-420\right)±\sqrt{\left(-420\right)^{2}-4\left(-3\right)\times 44100}}{2\left(-3\right)}$$

Pūrua -420.

$$x=\frac{-\left(-420\right)±\sqrt{176400-4\left(-3\right)\times 44100}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-\left(-420\right)±\sqrt{176400+12\times 44100}}{2\left(-3\right)}$$

Whakareatia 12 ki te 44100.

$$x=\frac{-\left(-420\right)±\sqrt{176400+529200}}{2\left(-3\right)}$$

Tāpiri 176400 ki te 529200.

$$x=\frac{-\left(-420\right)±\sqrt{705600}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 705600.

$$x=\frac{-\left(-420\right)±840}{2\left(-3\right)}$$

Ko te tauaro o -420 ko 420.

$$x=\frac{420±840}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{420±840}{-6}$$

Nā, me whakaoti te whārite x=\frac{420±840}{-6} ina he tāpiri te ±. Tāpiri 420 ki te 840.

$$x=\frac{1260}{-6}$$

Whakawehe 1260 ki te -6.

$$x=-210$$

Nā, me whakaoti te whārite x=\frac{420±840}{-6} ina he tango te ±. Tango 840 mai i 420.

$$x=-\frac{420}{-6}$$

Whakawehe -420 ki te -6.

$$x=70$$

Kua oti te whārite te whakatau.

$$x=-210 x=70$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,210 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-210\right), arā, te tauraro pātahi he tino iti rawa te kitea o 210-x,2x.

$$-2x\times 2x=\left(x-210\right)\left(210-x\right)$$

Whakareatia te -2 ki te 2, ka -4.

$$-4xx=\left(x-210\right)\left(210-x\right)$$

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

$$-4x^{2}=\left(x-210\right)\left(210-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-210 ki te 210-x ka whakakotahi i ngā kupu rite.

$$-4x^{2}=420x-x^{2}-44100$$

Tangohia te 420x mai i ngā taha e rua.

$$-4x^{2}-420x=-x^{2}-44100$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$-4x^{2}-420x+x^{2}=-44100$$

Pahekotia te -4x^{2} me x^{2}, ka -3x^{2}.

$$-3x^{2}-420x=-44100$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}-420x}{-3}=-\frac{44100}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x^{2}+\left(-\frac{420}{-3}\right)x=-\frac{44100}{-3}$$

Whakawehe -420 ki te -3.

$$x^{2}+140x=-\frac{44100}{-3}$$

Whakawehe -44100 ki te -3.

$$x^{2}+140x=14700$$

Whakawehea te 140, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 70. Nā, tāpiria te pūrua o te 70 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+140x+70^{2}=14700+70^{2}$$

Pūrua 70.

$$x^{2}+140x+4900=14700+4900$$

Tāpiri 14700 ki te 4900.

$$x^{2}+140x+4900=19600$$

Tauwehea x^{2}+140x+4900. 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}.

$$\left(x+70\right)^{2}=19600$$

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

$$\sqrt{\left(x+70\right)^{2}}=\sqrt{19600}$$

Whakarūnātia.

$$x+70=140 x+70=-140$$

Me tango 70 mai i ngā taha e rua o te whārite.

$$x=70 x=-210$$