Whakaoti i te 75/2x=2x/3

$$\frac { 75 } { 2 x } = \frac { 2 x } { 3 }$$

Whakaoti mō x

$$x = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 6x, arā, te tauraro pātahi he tino iti rawa te kitea o 2x,3.

$$3\times 75=2x\times 2x$$

Whakareatia te 2x ki te 2x, ka \left(2x\right)^{2}.

$$3\times 75=\left(2x\right)^{2}$$

Whakareatia te 3 ki te 75, ka 225.

$$225=\left(2x\right)^{2}$$

Whakarohaina te \left(2x\right)^{2}.

$$225=2^{2}x^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$225=4x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$4x^{2}=225$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{225}{4}$$

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

$$x=\frac{15}{2} x=-\frac{15}{2}$$

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. Me whakarea ngā taha e rua o te whārite ki te 6x, arā, te tauraro pātahi he tino iti rawa te kitea o 2x,3.

$$3\times 75=2x\times 2x$$

Whakareatia te 2x ki te 2x, ka \left(2x\right)^{2}.

$$3\times 75=\left(2x\right)^{2}$$

Whakareatia te 3 ki te 75, ka 225.

$$225=\left(2x\right)^{2}$$

Whakarohaina te \left(2x\right)^{2}.

$$225=2^{2}x^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$225=4x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$4x^{2}=225$$

Tangohia te 225 mai i ngā taha e rua.

$$4x^{2}-225=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -225 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-225\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-225\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-225\right)}}{2\times 4}$$

Whakareatia -16 ki te -225.

$$x=\frac{0±\sqrt{3600}}{2\times 4}$$

Tuhia te pūtakerua o te 3600.

$$x=\frac{0±60}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±60}{8}$$

Nā, me whakaoti te whārite x=\frac{0±60}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{60}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{15}{2}$$

Nā, me whakaoti te whārite x=\frac{0±60}{8} ina he tango te ±. Whakahekea te hautanga \frac{-60}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{15}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{15}{2} x=-\frac{15}{2}$$