Whakaoti i te 2x^2-8x-2.23=0

$$2 x ^ { 2 } - 8 x - 2.23 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{2046}}{20}+2\approx 4.261636576$$

$$x=-\frac{\sqrt{2046}}{20}+2\approx -0.261636576$$

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.

$$2x^{2}-8x-2.23=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -8 mō b, me -2.23 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-2.23\right)}}{2\times 2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-2.23\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-2.23\right)}}{2\times 2}$$

Whakareatia -8 ki te -2.23.

$$x=\frac{-\left(-8\right)±\sqrt{64+17.84}}{2\times 2}$$

Tāpiri 64 ki te 17.84.

$$x=\frac{-\left(-8\right)±\sqrt{81.84}}{2\times 2}$$

Tuhia te pūtakerua o te 81.84.

$$x=\frac{-\left(-8\right)±\frac{\sqrt{2046}}{5}}{2\times 2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±\frac{\sqrt{2046}}{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{8±\frac{\sqrt{2046}}{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{8±\frac{\sqrt{2046}}{5}}{4} ina he tāpiri te ±. Tāpiri 8 ki te \frac{\sqrt{2046}}{5}.

$$x=\frac{\frac{\sqrt{2046}}{5}+8}{4}$$

Whakawehe 8+\frac{\sqrt{2046}}{5} ki te 4.

$$x=\frac{\sqrt{2046}}{20}+2$$

Nā, me whakaoti te whārite x=\frac{8±\frac{\sqrt{2046}}{5}}{4} ina he tango te ±. Tango \frac{\sqrt{2046}}{5} mai i 8.

$$x=\frac{-\frac{\sqrt{2046}}{5}+8}{4}$$

Whakawehe 8-\frac{\sqrt{2046}}{5} ki te 4.

$$x=-\frac{\sqrt{2046}}{20}+2$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{2046}}{20}+2 x=-\frac{\sqrt{2046}}{20}+2$$

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.

$$2x^{2}-8x-2.23=0$$

Me tāpiri 2.23 ki ngā taha e rua o te whārite.

$$2x^{2}-8x-2.23-\left(-2.23\right)=-\left(-2.23\right)$$

Mā te tango i te -2.23 i a ia ake anō ka toe ko te 0.

$$2x^{2}-8x=-\left(-2.23\right)$$

Tango -2.23 mai i 0.

$$2x^{2}-8x=2.23$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-8x}{2}=\frac{2.23}{2}$$

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

$$x^{2}+\left(-\frac{8}{2}\right)x=\frac{2.23}{2}$$

Whakawehe -8 ki te 2.

$$x^{2}-4x=\frac{2.23}{2}$$

Whakawehe 2.23 ki te 2.

$$x^{2}-4x=1.115$$

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.

$$x^{2}-4x+\left(-2\right)^{2}=1.115+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=1.115+4$$

Tāpiri 1.115 ki te 4.

$$x^{2}-4x+4=5.115$$

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}.

$$\left(x-2\right)^{2}=5.115$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{5.115}$$

Whakarūnātia.

$$x-2=\frac{\sqrt{2046}}{20} x-2=-\frac{\sqrt{2046}}{20}$$

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

$$x=\frac{\sqrt{2046}}{20}+2 x=-\frac{\sqrt{2046}}{20}+2$$