Whakaoti i te 150x-x^2=(1-08832)100*50

$$150x- { x }^{ 2 } =(1-08832)100 \times 50$$

Whakaoti mō x

$$x=50$$

$$x=100$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 8832, ka 0.

$$150x-x^{2}=\left(1-0\right)\times 100\times 50$$

Tangohia te 0 i te 1, ka 1.

$$150x-x^{2}=1\times 100\times 50$$

Whakareatia te 1 ki te 100, ka 100.

$$150x-x^{2}=100\times 50$$

Whakareatia te 100 ki te 50, ka 5000.

$$150x-x^{2}=5000$$

Tangohia te 5000 mai i ngā taha e rua.

$$150x-x^{2}-5000=0$$

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.

$$-x^{2}+150x-5000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 150 mō b, me -5000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-150±\sqrt{150^{2}-4\left(-1\right)\left(-5000\right)}}{2\left(-1\right)}$$

Pūrua 150.

$$x=\frac{-150±\sqrt{22500-4\left(-1\right)\left(-5000\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-150±\sqrt{22500+4\left(-5000\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -5000.

$$x=\frac{-150±\sqrt{22500-20000}}{2\left(-1\right)}$$

Tāpiri 22500 ki te -20000.

$$x=\frac{-150±\sqrt{2500}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 2500.

$$x=\frac{-150±50}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-150±50}{-2}$$

Nā, me whakaoti te whārite x=\frac{-150±50}{-2} ina he tāpiri te ±. Tāpiri -150 ki te 50.

$$x=-\frac{100}{-2}$$

Whakawehe -100 ki te -2.

$$x=50$$

Nā, me whakaoti te whārite x=\frac{-150±50}{-2} ina he tango te ±. Tango 50 mai i -150.

$$x=-\frac{200}{-2}$$

Whakawehe -200 ki te -2.

$$x=100$$

Kua oti te whārite te whakatau.

$$x=50 x=100$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 8832, ka 0.

$$150x-x^{2}=\left(1-0\right)\times 100\times 50$$

Tangohia te 0 i te 1, ka 1.

$$150x-x^{2}=1\times 100\times 50$$

Whakareatia te 1 ki te 100, ka 100.

$$150x-x^{2}=100\times 50$$

Whakareatia te 100 ki te 50, ka 5000.

$$150x-x^{2}=5000$$

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.

$$-x^{2}+150x=5000$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+150x}{-1}=\frac{5000}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{150}{-1}x=\frac{5000}{-1}$$

Whakawehe 150 ki te -1.

$$x^{2}-150x=\frac{5000}{-1}$$

Whakawehe 5000 ki te -1.

$$x^{2}-150x=-5000$$

Whakawehea te -150, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -75. Nā, tāpiria te pūrua o te -75 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-150x+\left(-75\right)^{2}=-5000+\left(-75\right)^{2}$$

Pūrua -75.

$$x^{2}-150x+5625=-5000+5625$$

Tāpiri -5000 ki te 5625.

$$x^{2}-150x+5625=625$$

Tauwehea x^{2}-150x+5625. 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}.

$$\left(x-75\right)^{2}=625$$

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

$$\sqrt{\left(x-75\right)^{2}}=\sqrt{625}$$

Whakarūnātia.

$$x-75=25 x-75=-25$$

Me tāpiri 75 ki ngā taha e rua o te whārite.

$$x=100 x=50$$