Whakaoti i te left(40-30+xright)left(600-10xright)=10000

$$\left( 40-30+x \right) \left( 600-10x \right) = 10000$$

Whakaoti mō x

$$x=10$$

$$x=40$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 30 i te 40, ka 10.

$$\left(10+x\right)\left(600-10x\right)=10000$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 10+x ki te 600-10x ka whakakotahi i ngā kupu rite.

$$6000+500x-10x^{2}=10000$$

Tangohia te 10000 mai i ngā taha e rua.

$$6000+500x-10x^{2}-10000=0$$

Tangohia te 10000 i te 6000, ka -4000.

$$-4000+500x-10x^{2}=0$$

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.

$$-10x^{2}+500x-4000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -10 mō a, 500 mō b, me -4000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-500±\sqrt{500^{2}-4\left(-10\right)\left(-4000\right)}}{2\left(-10\right)}$$

Pūrua 500.

$$x=\frac{-500±\sqrt{250000-4\left(-10\right)\left(-4000\right)}}{2\left(-10\right)}$$

Whakareatia -4 ki te -10.

$$x=\frac{-500±\sqrt{250000+40\left(-4000\right)}}{2\left(-10\right)}$$

Whakareatia 40 ki te -4000.

$$x=\frac{-500±\sqrt{250000-160000}}{2\left(-10\right)}$$

Tāpiri 250000 ki te -160000.

$$x=\frac{-500±\sqrt{90000}}{2\left(-10\right)}$$

Tuhia te pūtakerua o te 90000.

$$x=\frac{-500±300}{2\left(-10\right)}$$

Whakareatia 2 ki te -10.

$$x=\frac{-500±300}{-20}$$

Nā, me whakaoti te whārite x=\frac{-500±300}{-20} ina he tāpiri te ±. Tāpiri -500 ki te 300.

$$x=-\frac{200}{-20}$$

Whakawehe -200 ki te -20.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{-500±300}{-20} ina he tango te ±. Tango 300 mai i -500.

$$x=-\frac{800}{-20}$$

Whakawehe -800 ki te -20.

$$x=40$$

Kua oti te whārite te whakatau.

$$x=10 x=40$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 30 i te 40, ka 10.

$$\left(10+x\right)\left(600-10x\right)=10000$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 10+x ki te 600-10x ka whakakotahi i ngā kupu rite.

$$6000+500x-10x^{2}=10000$$

Tangohia te 6000 mai i ngā taha e rua.

$$500x-10x^{2}=10000-6000$$

Tangohia te 6000 i te 10000, ka 4000.

$$500x-10x^{2}=4000$$

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.

$$-10x^{2}+500x=4000$$

Whakawehea ngā taha e rua ki te -10.

$$\frac{-10x^{2}+500x}{-10}=\frac{4000}{-10}$$

Mā te whakawehe ki te -10 ka wetekia te whakareanga ki te -10.

$$x^{2}+\frac{500}{-10}x=\frac{4000}{-10}$$

Whakawehe 500 ki te -10.

$$x^{2}-50x=\frac{4000}{-10}$$

Whakawehe 4000 ki te -10.

$$x^{2}-50x=-400$$

Whakawehea te -50, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -25. Nā, tāpiria te pūrua o te -25 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-50x+\left(-25\right)^{2}=-400+\left(-25\right)^{2}$$

Pūrua -25.

$$x^{2}-50x+625=-400+625$$

Tāpiri -400 ki te 625.

$$x^{2}-50x+625=225$$

Tauwehea x^{2}-50x+625. 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}.

$$\left(x-25\right)^{2}=225$$

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

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{225}$$

Whakarūnātia.

$$x-25=15 x-25=-15$$

Me tāpiri 25 ki ngā taha e rua o te whārite.

$$x=40 x=10$$