Whakaoti i te 6/x=2x+4/5

$$\frac { 6 } { x } = \frac { 2 x + 4 } { 5 }$$

Whakaoti mō x

$$x=-5$$

$$x=3$$

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 5x, arā, te tauraro pātahi he tino iti rawa te kitea o x,5.

$$5\times 6=x\left(2x+4\right)$$

Whakareatia te 5 ki te 6, ka 30.

$$30=x\left(2x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 2x+4.

$$30=2x^{2}+4x$$

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

$$2x^{2}+4x=30$$

Tangohia te 30 mai i ngā taha e rua.

$$2x^{2}+4x-30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 4 mō b, me -30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\times 2\left(-30\right)}}{2\times 2}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\times 2\left(-30\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-4±\sqrt{16-8\left(-30\right)}}{2\times 2}$$

Whakareatia -8 ki te -30.

$$x=\frac{-4±\sqrt{16+240}}{2\times 2}$$

Tāpiri 16 ki te 240.

$$x=\frac{-4±\sqrt{256}}{2\times 2}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-4±16}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-4±16}{4}$$

Nā, me whakaoti te whārite x=\frac{-4±16}{4} ina he tāpiri te ±. Tāpiri -4 ki te 16.

$$x=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{-4±16}{4} ina he tango te ±. Tango 16 mai i -4.

$$x=-\frac{20}{4}$$

Whakawehe -20 ki te 4.

$$x=-5$$

Kua oti te whārite te whakatau.

$$x=3 x=-5$$

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. Me whakarea ngā taha e rua o te whārite ki te 5x, arā, te tauraro pātahi he tino iti rawa te kitea o x,5.

$$5\times 6=x\left(2x+4\right)$$

Whakareatia te 5 ki te 6, ka 30.

$$30=x\left(2x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 2x+4.

$$30=2x^{2}+4x$$

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

$$2x^{2}+4x=30$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+4x}{2}=\frac{30}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{4}{2}x=\frac{30}{2}$$

Whakawehe 4 ki te 2.

$$x^{2}+2x=\frac{30}{2}$$

Whakawehe 30 ki te 2.

$$x^{2}+2x=15$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=15+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=15+1$$

Tāpiri 15 ki te 1.

$$x^{2}+2x+1=16$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=16$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x+1=4 x+1=-4$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=3 x=-5$$