Whakaoti i te 72=2x^2+8x

$$72 = 2 x ^ { 2 } + 8 x$$

Whakaoti mō x

$$x=2\sqrt{10}-2\approx 4.32455532$$

$$x=-2\sqrt{10}-2\approx -8.32455532$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2x^{2}+8x=72$$

Tangohia te 72 mai i ngā taha e rua.

$$2x^{2}+8x-72=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 8 mō b, me -72 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2\left(-72\right)}}{2\times 2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 2\left(-72\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-8±\sqrt{64-8\left(-72\right)}}{2\times 2}$$

Whakareatia -8 ki te -72.

$$x=\frac{-8±\sqrt{64+576}}{2\times 2}$$

Tāpiri 64 ki te 576.

$$x=\frac{-8±\sqrt{640}}{2\times 2}$$

Tuhia te pūtakerua o te 640.

$$x=\frac{-8±8\sqrt{10}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-8±8\sqrt{10}}{4}$$

Nā, me whakaoti te whārite x=\frac{-8±8\sqrt{10}}{4} ina he tāpiri te ±. Tāpiri -8 ki te 8\sqrt{10}.

$$x=\frac{8\sqrt{10}-8}{4}$$

Whakawehe -8+8\sqrt{10} ki te 4.

$$x=2\sqrt{10}-2$$

Nā, me whakaoti te whārite x=\frac{-8±8\sqrt{10}}{4} ina he tango te ±. Tango 8\sqrt{10} mai i -8.

$$x=\frac{-8\sqrt{10}-8}{4}$$

Whakawehe -8-8\sqrt{10} ki te 4.

$$x=-2\sqrt{10}-2$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{10}-2 x=-2\sqrt{10}-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2x^{2}+8x=72$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+8x}{2}=\frac{72}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{8}{2}x=\frac{72}{2}$$

Whakawehe 8 ki te 2.

$$x^{2}+4x=\frac{72}{2}$$

Whakawehe 72 ki te 2.

$$x^{2}+4x=36$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+4x+2^{2}=36+2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=36+4$$

Tāpiri 36 ki te 4.

$$x^{2}+4x+4=40$$

Tauwehea x^{2}+4x+4. 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}.

$$\left(x+2\right)^{2}=40$$

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{40}$$

Whakarūnātia.

$$x+2=2\sqrt{10} x+2=-2\sqrt{10}$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{10}-2 x=-2\sqrt{10}-2$$