Whakaoti i te 9=2x(-5-x/2)

$$9=2x(-5- \frac{ x }{ 2 } )$$

Whakaoti mō x

$$x=-9$$

$$x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$18=4x\left(-5-\frac{x}{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te -5-\frac{x}{2}.

$$18=-20x+4x\left(-\frac{x}{2}\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 4 me te 2.

$$18=-20x-2xx$$

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

$$18=-20x-2x^{2}$$

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

$$-20x-2x^{2}=18$$

Tangohia te 18 mai i ngā taha e rua.

$$-20x-2x^{2}-18=0$$

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.

$$-2x^{2}-20x-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, -20 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\left(-2\right)\left(-18\right)}}{2\left(-2\right)}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\left(-2\right)\left(-18\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-20\right)±\sqrt{400+8\left(-18\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -18.

$$x=\frac{-\left(-20\right)±\sqrt{400-144}}{2\left(-2\right)}$$

Tāpiri 400 ki te -144.

$$x=\frac{-\left(-20\right)±\sqrt{256}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-\left(-20\right)±16}{2\left(-2\right)}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±16}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{20±16}{-4}$$

Nā, me whakaoti te whārite x=\frac{20±16}{-4} ina he tāpiri te ±. Tāpiri 20 ki te 16.

$$x=\frac{36}{-4}$$

Whakawehe 36 ki te -4.

$$x=-9$$

Nā, me whakaoti te whārite x=\frac{20±16}{-4} ina he tango te ±. Tango 16 mai i 20.

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

Whakawehe 4 ki te -4.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=-9 x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$18=4x\left(-5-\frac{x}{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te -5-\frac{x}{2}.

$$18=-20x+4x\left(-\frac{x}{2}\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 4 me te 2.

$$18=-20x-2xx$$

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

$$18=-20x-2x^{2}$$

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

$$-20x-2x^{2}=18$$

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.

$$-2x^{2}-20x=18$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}-20x}{-2}=\frac{18}{-2}$$

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

$$x^{2}+\left(-\frac{20}{-2}\right)x=\frac{18}{-2}$$

Whakawehe -20 ki te -2.

$$x^{2}+10x=\frac{18}{-2}$$

Whakawehe 18 ki te -2.

$$x^{2}+10x=-9$$

Whakawehea te 10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 5. Nā, tāpiria te pūrua o te 5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+10x+5^{2}=-9+5^{2}$$

Pūrua 5.

$$x^{2}+10x+25=-9+25$$

Tāpiri -9 ki te 25.

$$x^{2}+10x+25=16$$

Tauwehea x^{2}+10x+25. 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}.

$$\left(x+5\right)^{2}=16$$

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

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x+5=4 x+5=-4$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$x=-1 x=-9$$