Whakaoti i te 76x-76=x^2+8x

$$76 x - 76 = x ^ { 2 } + 8 x$$

Whakaoti mō x

$$x=6\sqrt{30}+34\approx 66.86335345$$

$$x=34-6\sqrt{30}\approx 1.13664655$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$76x-76-x^{2}=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$76x-76-x^{2}-8x=0$$

Pahekotia te 76x me -8x, ka 68x.

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

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.

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

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

$$x=\frac{-68±\sqrt{68^{2}-4\left(-1\right)\left(-76\right)}}{2\left(-1\right)}$$

Pūrua 68.

$$x=\frac{-68±\sqrt{4624-4\left(-1\right)\left(-76\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-68±\sqrt{4624+4\left(-76\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -76.

$$x=\frac{-68±\sqrt{4624-304}}{2\left(-1\right)}$$

Tāpiri 4624 ki te -304.

$$x=\frac{-68±\sqrt{4320}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 4320.

$$x=\frac{-68±12\sqrt{30}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-68±12\sqrt{30}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-68±12\sqrt{30}}{-2} ina he tāpiri te ±. Tāpiri -68 ki te 12\sqrt{30}.

$$x=\frac{12\sqrt{30}-68}{-2}$$

Whakawehe -68+12\sqrt{30} ki te -2.

$$x=34-6\sqrt{30}$$

Nā, me whakaoti te whārite x=\frac{-68±12\sqrt{30}}{-2} ina he tango te ±. Tango 12\sqrt{30} mai i -68.

$$x=\frac{-12\sqrt{30}-68}{-2}$$

Whakawehe -68-12\sqrt{30} ki te -2.

$$x=6\sqrt{30}+34$$

Kua oti te whārite te whakatau.

$$x=34-6\sqrt{30} x=6\sqrt{30}+34$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$76x-76-x^{2}=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$76x-76-x^{2}-8x=0$$

Pahekotia te 76x me -8x, ka 68x.

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

Me tāpiri te 76 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

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.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+68x}{-1}=\frac{76}{-1}$$

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

$$x^{2}+\frac{68}{-1}x=\frac{76}{-1}$$

Whakawehe 68 ki te -1.

$$x^{2}-68x=\frac{76}{-1}$$

Whakawehe 76 ki te -1.

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

Whakawehea te -68, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -34. Nā, tāpiria te pūrua o te -34 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-68x+\left(-34\right)^{2}=-76+\left(-34\right)^{2}$$

Pūrua -34.

$$x^{2}-68x+1156=-76+1156$$

Tāpiri -76 ki te 1156.

$$x^{2}-68x+1156=1080$$

Tauwehea x^{2}-68x+1156. 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}.

$$\left(x-34\right)^{2}=1080$$

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

$$\sqrt{\left(x-34\right)^{2}}=\sqrt{1080}$$

Whakarūnātia.

$$x-34=6\sqrt{30} x-34=-6\sqrt{30}$$

Me tāpiri 34 ki ngā taha e rua o te whārite.

$$x=6\sqrt{30}+34 x=34-6\sqrt{30}$$