Whakaoti i te 1280-72x-x^2=1140

$$1280 - 72 x - x ^ { 2 } = 1140$$

Whakaoti mō x

$$x=2\sqrt{359}-36\approx 1.894590643$$

$$x=-2\sqrt{359}-36\approx -73.894590643$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-x^{2}-72x+1280=1140$$

Me tango 1140 mai i ngā taha e rua o te whārite.

$$-x^{2}-72x+1280-1140=1140-1140$$

Mā te tango i te 1140 i a ia ake anō ka toe ko te 0.

$$-x^{2}-72x+1280-1140=0$$

Tango 1140 mai i 1280.

$$-x^{2}-72x+140=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -72 mō b, me 140 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\left(-1\right)\times 140}}{2\left(-1\right)}$$

Pūrua -72.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\left(-1\right)\times 140}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-72\right)±\sqrt{5184+4\times 140}}{2\left(-1\right)}$$

Whakareatia 4 ki te 140.

$$x=\frac{-\left(-72\right)±\sqrt{5184+560}}{2\left(-1\right)}$$

Tāpiri 5184 ki te 560.

$$x=\frac{-\left(-72\right)±\sqrt{5744}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 5744.

$$x=\frac{-\left(-72\right)±4\sqrt{359}}{2\left(-1\right)}$$

Ko te tauaro o -72 ko 72.

$$x=\frac{72±4\sqrt{359}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{72±4\sqrt{359}}{-2}$$

Nā, me whakaoti te whārite x=\frac{72±4\sqrt{359}}{-2} ina he tāpiri te ±. Tāpiri 72 ki te 4\sqrt{359}.

$$x=\frac{4\sqrt{359}+72}{-2}$$

Whakawehe 72+4\sqrt{359} ki te -2.

$$x=-2\sqrt{359}-36$$

Nā, me whakaoti te whārite x=\frac{72±4\sqrt{359}}{-2} ina he tango te ±. Tango 4\sqrt{359} mai i 72.

$$x=\frac{72-4\sqrt{359}}{-2}$$

Whakawehe 72-4\sqrt{359} ki te -2.

$$x=2\sqrt{359}-36$$

Kua oti te whārite te whakatau.

$$x=-2\sqrt{359}-36 x=2\sqrt{359}-36$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$-x^{2}-72x+1280=1140$$

Me tango 1280 mai i ngā taha e rua o te whārite.

$$-x^{2}-72x+1280-1280=1140-1280$$

Mā te tango i te 1280 i a ia ake anō ka toe ko te 0.

$$-x^{2}-72x=1140-1280$$

Tango 1280 mai i 1140.

$$-x^{2}-72x=-140$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-72x}{-1}=-\frac{140}{-1}$$

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

$$x^{2}+\left(-\frac{72}{-1}\right)x=-\frac{140}{-1}$$

Whakawehe -72 ki te -1.

$$x^{2}+72x=-\frac{140}{-1}$$

Whakawehe -140 ki te -1.

$$x^{2}+72x=140$$

Whakawehea te 72, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 36. Nā, tāpiria te pūrua o te 36 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+72x+36^{2}=140+36^{2}$$

Pūrua 36.

$$x^{2}+72x+1296=140+1296$$

Tāpiri 140 ki te 1296.

$$x^{2}+72x+1296=1436$$

Tauwehea x^{2}+72x+1296. 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}.

$$\left(x+36\right)^{2}=1436$$

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

$$\sqrt{\left(x+36\right)^{2}}=\sqrt{1436}$$

Whakarūnātia.

$$x+36=2\sqrt{359} x+36=-2\sqrt{359}$$

Me tango 36 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{359}-36 x=-2\sqrt{359}-36$$