Whakaoti i te 6/2x+4=x-5/10

$$\frac { 6 } { 2 x + 4 } = \frac { x - 5 } { 10 }$$

Whakaoti mō x

$$x=-5$$

$$x=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x+4,10.

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

Whakareatia te 5 ki te 6, ka 30.

$$30=\left(x+2\right)\left(x-5\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x-5 ka whakakotahi i ngā kupu rite.

$$30=x^{2}-3x-10$$

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

$$x^{2}-3x-10=30$$

Tangohia te 30 mai i ngā taha e rua.

$$x^{2}-3x-10-30=0$$

Tangohia te 30 i te -10, ka -40.

$$x^{2}-3x-40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me -40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-40\right)}}{2}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-40\right)}}{2}$$

Whakareatia -4 ki te -40.

$$x=\frac{-\left(-3\right)±\sqrt{9+160}}{2}$$

Tāpiri 9 ki te 160.

$$x=\frac{-\left(-3\right)±\sqrt{169}}{2}$$

Tuhia te pūtakerua o te 169.

$$x=\frac{-\left(-3\right)±13}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±13}{2}$$

Nā, me whakaoti te whārite x=\frac{3±13}{2} ina he tāpiri te ±. Tāpiri 3 ki te 13.

$$x=\frac{16}{2}$$

Whakawehe 16 ki te 2.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{3±13}{2} ina he tango te ±. Tango 13 mai i 3.

$$x=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$x=-5$$

Kua oti te whārite te whakatau.

$$x=8 x=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x+4,10.

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

Whakareatia te 5 ki te 6, ka 30.

$$30=\left(x+2\right)\left(x-5\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x-5 ka whakakotahi i ngā kupu rite.

$$30=x^{2}-3x-10$$

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

$$x^{2}-3x-10=30$$

Me tāpiri te 10 ki ngā taha e rua.

$$x^{2}-3x=30+10$$

Tāpirihia te 30 ki te 10, ka 40.

$$x^{2}-3x=40$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=40+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=40+\frac{9}{4}$$

Tāpiri 40 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{169}{4}$$

Tauwehea x^{2}-3x+\frac{9}{4}. 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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{169}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{169}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{13}{2} x-\frac{3}{2}=-\frac{13}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=8 x=-5$$