Whakaoti i te 8q(q-2)+10=0

$$8 q ( q - 2 ) + 10 = 0$$

Whakaoti mō q

$$q=1+\frac{1}{2}i=1+0.5i$$

$$q=1-\frac{1}{2}i=1-0.5i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 8q ki te q-2.

$$8q^{2}-16q+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -16 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 8\times 10}}{2\times 8}$$

Pūrua -16.

$$q=\frac{-\left(-16\right)±\sqrt{256-4\times 8\times 10}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$q=\frac{-\left(-16\right)±\sqrt{256-32\times 10}}{2\times 8}$$

Whakareatia -32 ki te 10.

$$q=\frac{-\left(-16\right)±\sqrt{256-320}}{2\times 8}$$

Tāpiri 256 ki te -320.

$$q=\frac{-\left(-16\right)±\sqrt{-64}}{2\times 8}$$

Tuhia te pūtakerua o te -64.

$$q=\frac{-\left(-16\right)±8i}{2\times 8}$$

Ko te tauaro o -16 ko 16.

$$q=\frac{16±8i}{2\times 8}$$

Whakareatia 2 ki te 8.

$$q=\frac{16±8i}{16}$$

Nā, me whakaoti te whārite q=\frac{16±8i}{16} ina he tāpiri te ±. Tāpiri 16 ki te 8i.

$$q=\frac{16+8i}{16}$$

Whakawehe 16+8i ki te 16.

$$q=1+\frac{1}{2}i$$

Nā, me whakaoti te whārite q=\frac{16±8i}{16} ina he tango te ±. Tango 8i mai i 16.

$$q=\frac{16-8i}{16}$$

Whakawehe 16-8i ki te 16.

$$q=1-\frac{1}{2}i$$

Kua oti te whārite te whakatau.

$$q=1+\frac{1}{2}i q=1-\frac{1}{2}i$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 8q ki te q-2.

$$8q^{2}-16q+10=0$$

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$8q^{2}-16q=-10$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8q^{2}-16q}{8}=-\frac{10}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$q^{2}+\left(-\frac{16}{8}\right)q=-\frac{10}{8}$$

Whakawehe -16 ki te 8.

$$q^{2}-2q=-\frac{10}{8}$$

Whakahekea te hautanga \frac{-10}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$q^{2}-2q=-\frac{5}{4}$$

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}-2q+1=-\frac{5}{4}+1$$

Tāpiri -\frac{5}{4} ki te 1.

$$q^{2}-2q+1=-\frac{1}{4}$$

Tauwehea q^{2}-2q+1. 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}.

$$\left(q-1\right)^{2}=-\frac{1}{4}$$

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

$$\sqrt{\left(q-1\right)^{2}}=\sqrt{-\frac{1}{4}}$$

Whakarūnātia.

$$q-1=\frac{1}{2}i q-1=-\frac{1}{2}i$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$q=1+\frac{1}{2}i q=1-\frac{1}{2}i$$