Whakaoti i te (20-5x)(6-x)=12.5*6

$$( 20 - 5 x ) ( 6 - x ) = 12.5 \times 6$$

Whakaoti mō x

$$x=1$$

$$x=9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 20-5x ki te 6-x ka whakakotahi i ngā kupu rite.

$$120-50x+5x^{2}=12.5\times 6$$

Whakareatia te 12.5 ki te 6, ka 75.

$$120-50x+5x^{2}=75$$

Tangohia te 75 mai i ngā taha e rua.

$$120-50x+5x^{2}-75=0$$

Tangohia te 75 i te 120, ka 45.

$$45-50x+5x^{2}=0$$

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.

$$5x^{2}-50x+45=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -50 mō b, me 45 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 5\times 45}}{2\times 5}$$

Pūrua -50.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 5\times 45}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-50\right)±\sqrt{2500-20\times 45}}{2\times 5}$$

Whakareatia -20 ki te 45.

$$x=\frac{-\left(-50\right)±\sqrt{2500-900}}{2\times 5}$$

Tāpiri 2500 ki te -900.

$$x=\frac{-\left(-50\right)±\sqrt{1600}}{2\times 5}$$

Tuhia te pūtakerua o te 1600.

$$x=\frac{-\left(-50\right)±40}{2\times 5}$$

Ko te tauaro o -50 ko 50.

$$x=\frac{50±40}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{50±40}{10}$$

Nā, me whakaoti te whārite x=\frac{50±40}{10} ina he tāpiri te ±. Tāpiri 50 ki te 40.

$$x=\frac{90}{10}$$

Whakawehe 90 ki te 10.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{50±40}{10} ina he tango te ±. Tango 40 mai i 50.

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

Whakawehe 10 ki te 10.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=9 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 20-5x ki te 6-x ka whakakotahi i ngā kupu rite.

$$120-50x+5x^{2}=12.5\times 6$$

Whakareatia te 12.5 ki te 6, ka 75.

$$120-50x+5x^{2}=75$$

Tangohia te 120 mai i ngā taha e rua.

$$-50x+5x^{2}=75-120$$

Tangohia te 120 i te 75, ka -45.

$$-50x+5x^{2}=-45$$

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.

$$5x^{2}-50x=-45$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-50x}{5}=-\frac{45}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}+\left(-\frac{50}{5}\right)x=-\frac{45}{5}$$

Whakawehe -50 ki te 5.

$$x^{2}-10x=-\frac{45}{5}$$

Whakawehe -45 ki te 5.

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

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.

$$x^{2}-10x+\left(-5\right)^{2}=-9+\left(-5\right)^{2}$$

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 tāpiri 5 ki ngā taha e rua o te whārite.

$$x=9 x=1$$