Whakaoti i te 2x^2-8x-2*26=0

$$2 { x }^{ 2 } -8x-2 \times 26=0$$

Whakaoti mō x

$$x=\sqrt{30}+2\approx 7.477225575$$

$$x=2-\sqrt{30}\approx -3.477225575$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 2 ki te 26, ka 52.

$$2x^{2}-8x-52=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -8 mō b, me -52 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-52\right)}}{2\times 2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-52\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-52\right)}}{2\times 2}$$

Whakareatia -8 ki te -52.

$$x=\frac{-\left(-8\right)±\sqrt{64+416}}{2\times 2}$$

Tāpiri 64 ki te 416.

$$x=\frac{-\left(-8\right)±\sqrt{480}}{2\times 2}$$

Tuhia te pūtakerua o te 480.

$$x=\frac{-\left(-8\right)±4\sqrt{30}}{2\times 2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±4\sqrt{30}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{8±4\sqrt{30}}{4}$$

Nā, me whakaoti te whārite x=\frac{8±4\sqrt{30}}{4} ina he tāpiri te ±. Tāpiri 8 ki te 4\sqrt{30}.

$$x=\frac{4\sqrt{30}+8}{4}$$

Whakawehe 8+4\sqrt{30} ki te 4.

$$x=\sqrt{30}+2$$

Nā, me whakaoti te whārite x=\frac{8±4\sqrt{30}}{4} ina he tango te ±. Tango 4\sqrt{30} mai i 8.

$$x=\frac{8-4\sqrt{30}}{4}$$

Whakawehe 8-4\sqrt{30} ki te 4.

$$x=2-\sqrt{30}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{30}+2 x=2-\sqrt{30}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 2 ki te 26, ka 52.

$$2x^{2}-8x-52=0$$

Me tāpiri te 52 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2x^{2}-8x=52$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-8x}{2}=\frac{52}{2}$$

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

$$x^{2}+\left(-\frac{8}{2}\right)x=\frac{52}{2}$$

Whakawehe -8 ki te 2.

$$x^{2}-4x=\frac{52}{2}$$

Whakawehe 52 ki te 2.

$$x^{2}-4x=26$$

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.

$$x^{2}-4x+\left(-2\right)^{2}=26+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=26+4$$

Tāpiri 26 ki te 4.

$$x^{2}-4x+4=30$$

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}.

$$\left(x-2\right)^{2}=30$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{30}$$

Whakarūnātia.

$$x-2=\sqrt{30} x-2=-\sqrt{30}$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=\sqrt{30}+2 x=2-\sqrt{30}$$