Whakaoti i te (10+x)(730-x)=1000

$$( 10 + x ) ( 730 - x ) = 1000$$

Whakaoti mō x

$$x=30\sqrt{151}+360\approx 728.646171823$$

$$x=360-30\sqrt{151}\approx -8.646171823$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 10+x ki te 730-x ka whakakotahi i ngā kupu rite.

$$7300+720x-x^{2}=1000$$

Tangohia te 1000 mai i ngā taha e rua.

$$7300+720x-x^{2}-1000=0$$

Tangohia te 1000 i te 7300, ka 6300.

$$6300+720x-x^{2}=0$$

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.

$$-x^{2}+720x+6300=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 720 mō b, me 6300 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-720±\sqrt{720^{2}-4\left(-1\right)\times 6300}}{2\left(-1\right)}$$

Pūrua 720.

$$x=\frac{-720±\sqrt{518400-4\left(-1\right)\times 6300}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-720±\sqrt{518400+4\times 6300}}{2\left(-1\right)}$$

Whakareatia 4 ki te 6300.

$$x=\frac{-720±\sqrt{518400+25200}}{2\left(-1\right)}$$

Tāpiri 518400 ki te 25200.

$$x=\frac{-720±\sqrt{543600}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 543600.

$$x=\frac{-720±60\sqrt{151}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-720±60\sqrt{151}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-720±60\sqrt{151}}{-2} ina he tāpiri te ±. Tāpiri -720 ki te 60\sqrt{151}.

$$x=\frac{60\sqrt{151}-720}{-2}$$

Whakawehe -720+60\sqrt{151} ki te -2.

$$x=360-30\sqrt{151}$$

Nā, me whakaoti te whārite x=\frac{-720±60\sqrt{151}}{-2} ina he tango te ±. Tango 60\sqrt{151} mai i -720.

$$x=\frac{-60\sqrt{151}-720}{-2}$$

Whakawehe -720-60\sqrt{151} ki te -2.

$$x=30\sqrt{151}+360$$

Kua oti te whārite te whakatau.

$$x=360-30\sqrt{151} x=30\sqrt{151}+360$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 10+x ki te 730-x ka whakakotahi i ngā kupu rite.

$$7300+720x-x^{2}=1000$$

Tangohia te 7300 mai i ngā taha e rua.

$$720x-x^{2}=1000-7300$$

Tangohia te 7300 i te 1000, ka -6300.

$$720x-x^{2}=-6300$$

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.

$$-x^{2}+720x=-6300$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+720x}{-1}=-\frac{6300}{-1}$$

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

$$x^{2}+\frac{720}{-1}x=-\frac{6300}{-1}$$

Whakawehe 720 ki te -1.

$$x^{2}-720x=-\frac{6300}{-1}$$

Whakawehe -6300 ki te -1.

$$x^{2}-720x=6300$$

Whakawehea te -720, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -360. Nā, tāpiria te pūrua o te -360 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-720x+\left(-360\right)^{2}=6300+\left(-360\right)^{2}$$

Pūrua -360.

$$x^{2}-720x+129600=6300+129600$$

Tāpiri 6300 ki te 129600.

$$x^{2}-720x+129600=135900$$

Tauwehea x^{2}-720x+129600. 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}.

$$\left(x-360\right)^{2}=135900$$

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

$$\sqrt{\left(x-360\right)^{2}}=\sqrt{135900}$$

Whakarūnātia.

$$x-360=30\sqrt{151} x-360=-30\sqrt{151}$$

Me tāpiri 360 ki ngā taha e rua o te whārite.

$$x=30\sqrt{151}+360 x=360-30\sqrt{151}$$