Whakaoti i te left(50-xright)x=600

$$\left( 50-x \right) x = 600$$

Whakaoti mō x

$$x=20$$

$$x=30$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 50-x ki te x.

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

Tangohia te 600 mai i ngā taha e rua.

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

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.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 50 mō b, me -600 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-50±\sqrt{50^{2}-4\left(-1\right)\left(-600\right)}}{2\left(-1\right)}$$

Pūrua 50.

$$x=\frac{-50±\sqrt{2500-4\left(-1\right)\left(-600\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-50±\sqrt{2500+4\left(-600\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -600.

$$x=\frac{-50±\sqrt{2500-2400}}{2\left(-1\right)}$$

Tāpiri 2500 ki te -2400.

$$x=\frac{-50±\sqrt{100}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-50±10}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-50±10}{-2}$$

Nā, me whakaoti te whārite x=\frac{-50±10}{-2} ina he tāpiri te ±. Tāpiri -50 ki te 10.

$$x=-\frac{40}{-2}$$

Whakawehe -40 ki te -2.

$$x=20$$

Nā, me whakaoti te whārite x=\frac{-50±10}{-2} ina he tango te ±. Tango 10 mai i -50.

$$x=-\frac{60}{-2}$$

Whakawehe -60 ki te -2.

$$x=30$$

Kua oti te whārite te whakatau.

$$x=20 x=30$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 50-x ki te x.

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

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.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+50x}{-1}=\frac{600}{-1}$$

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

$$x^{2}+\frac{50}{-1}x=\frac{600}{-1}$$

Whakawehe 50 ki te -1.

$$x^{2}-50x=\frac{600}{-1}$$

Whakawehe 600 ki te -1.

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

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.

$$x^{2}-50x+\left(-25\right)^{2}=-600+\left(-25\right)^{2}$$

Pūrua -25.

$$x^{2}-50x+625=-600+625$$

Tāpiri -600 ki te 625.

$$x^{2}-50x+625=25$$

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}.

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

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

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

Whakarūnātia.

$$x-25=5 x-25=-5$$

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

$$x=30 x=20$$