Whakaoti i te x^2-76x=-68

$$x ^ { 2 } - 76 x = - 68$$

Whakaoti mō x

$$x=4\sqrt{86}+38\approx 75.094473982$$

$$x=38-4\sqrt{86}\approx 0.905526018$$

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.

$$x^{2}-76x=-68$$

Me tāpiri 68 ki ngā taha e rua o te whārite.

$$x^{2}-76x-\left(-68\right)=-68-\left(-68\right)$$

Mā te tango i te -68 i a ia ake anō ka toe ko te 0.

$$x^{2}-76x-\left(-68\right)=0$$

Tango -68 mai i 0.

$$x^{2}-76x+68=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -76 mō b, me 68 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-76\right)±\sqrt{\left(-76\right)^{2}-4\times 68}}{2}$$

Pūrua -76.

$$x=\frac{-\left(-76\right)±\sqrt{5776-4\times 68}}{2}$$

Whakareatia -4 ki te 68.

$$x=\frac{-\left(-76\right)±\sqrt{5776-272}}{2}$$

Tāpiri 5776 ki te -272.

$$x=\frac{-\left(-76\right)±\sqrt{5504}}{2}$$

Tuhia te pūtakerua o te 5504.

$$x=\frac{-\left(-76\right)±8\sqrt{86}}{2}$$

Ko te tauaro o -76 ko 76.

$$x=\frac{76±8\sqrt{86}}{2}$$

Nā, me whakaoti te whārite x=\frac{76±8\sqrt{86}}{2} ina he tāpiri te ±. Tāpiri 76 ki te 8\sqrt{86}.

$$x=\frac{8\sqrt{86}+76}{2}$$

Whakawehe 76+8\sqrt{86} ki te 2.

$$x=4\sqrt{86}+38$$

Nā, me whakaoti te whārite x=\frac{76±8\sqrt{86}}{2} ina he tango te ±. Tango 8\sqrt{86} mai i 76.

$$x=\frac{76-8\sqrt{86}}{2}$$

Whakawehe 76-8\sqrt{86} ki te 2.

$$x=38-4\sqrt{86}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{86}+38 x=38-4\sqrt{86}$$

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.

$$x^{2}-76x=-68$$

Whakawehea te -76, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -38. Nā, tāpiria te pūrua o te -38 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-76x+\left(-38\right)^{2}=-68+\left(-38\right)^{2}$$

Pūrua -38.

$$x^{2}-76x+1444=-68+1444$$

Tāpiri -68 ki te 1444.

$$x^{2}-76x+1444=1376$$

Tauwehea x^{2}-76x+1444. 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}.

$$\left(x-38\right)^{2}=1376$$

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

$$\sqrt{\left(x-38\right)^{2}}=\sqrt{1376}$$

Whakarūnātia.

$$x-38=4\sqrt{86} x-38=-4\sqrt{86}$$

Me tāpiri 38 ki ngā taha e rua o te whārite.

$$x=4\sqrt{86}+38 x=38-4\sqrt{86}$$