Whakaoti i te 600=100x-0.5x^2-50x+600

$$600 = 100 x - 0.5 x ^ { 2 } - 50 x + 600$$

Whakaoti mō x

$$x=100$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Pahekotia te 100x me -50x, ka 50x.

$$600=50x-0.5x^{2}+600$$

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

$$50x-0.5x^{2}+600=600$$

Tangohia te 600 mai i ngā taha e rua.

$$50x-0.5x^{2}+600-600=0$$

Tangohia te 600 i te 600, ka 0.

$$50x-0.5x^{2}=0$$

Tauwehea te x.

$$x\left(50-0.5x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 50-\frac{x}{2}=0.

$$x=0 x=100$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 100x me -50x, ka 50x.

$$600=50x-0.5x^{2}+600$$

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

$$50x-0.5x^{2}+600=600$$

Tangohia te 600 mai i ngā taha e rua.

$$50x-0.5x^{2}+600-600=0$$

Tangohia te 600 i te 600, ka 0.

$$50x-0.5x^{2}=0$$

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.

$$-0.5x^{2}+50x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -0.5 mō a, 50 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-50±\sqrt{50^{2}}}{2\left(-0.5\right)}$$

Tuhia te pūtakerua o te 50^{2}.

$$x=\frac{-50±50}{2\left(-0.5\right)}$$

Whakareatia 2 ki te -0.5.

$$x=\frac{-50±50}{-1}$$

Nā, me whakaoti te whārite x=\frac{-50±50}{-1} ina he tāpiri te ±. Tāpiri -50 ki te 50.

$$x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-50±50}{-1} ina he tango te ±. Tango 50 mai i -50.

$$x=-\frac{100}{-1}$$

Whakawehe -100 ki te -1.

$$x=100$$

Kua oti te whārite te whakatau.

$$x=0 x=100$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 100x me -50x, ka 50x.

$$600=50x-0.5x^{2}+600$$

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

$$50x-0.5x^{2}+600=600$$

Tangohia te 600 mai i ngā taha e rua.

$$50x-0.5x^{2}=600-600$$

Tangohia te 600 i te 600, ka 0.

$$50x-0.5x^{2}=0$$

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.

$$-0.5x^{2}+50x=0$$

Me whakarea ngā taha e rua ki te -2.

$$\frac{-0.5x^{2}+50x}{-0.5}=\frac{0}{-0.5}$$

Mā te whakawehe ki te -0.5 ka wetekia te whakareanga ki te -0.5.

$$x^{2}+\frac{50}{-0.5}x=\frac{0}{-0.5}$$

Whakawehe 50 ki te -0.5 mā te whakarea 50 ki te tau huripoki o -0.5.

$$x^{2}-100x=\frac{0}{-0.5}$$

Whakawehe 0 ki te -0.5 mā te whakarea 0 ki te tau huripoki o -0.5.

$$x^{2}-100x=0$$

Whakawehea te -100, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -50. Nā, tāpiria te pūrua o te -50 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-100x+\left(-50\right)^{2}=\left(-50\right)^{2}$$

Pūrua -50.

$$x^{2}-100x+2500=2500$$

Tauwehea x^{2}-100x+2500. 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}.

$$\left(x-50\right)^{2}=2500$$

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

$$\sqrt{\left(x-50\right)^{2}}=\sqrt{2500}$$

Whakarūnātia.

$$x-50=50 x-50=-50$$

Me tāpiri 50 ki ngā taha e rua o te whārite.

$$x=100 x=0$$