Whakaoti i te 0=8x^2+5+6x

$$0 = 8 x ^ { 2 } + 5 + 6 x$$

Whakaoti mō x (complex solution)

$$x=\frac{-3+\sqrt{31}i}{8}\approx -0.375+0.695970545i$$

$$x=\frac{-\sqrt{31}i-3}{8}\approx -0.375-0.695970545i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$8x^{2}+5+6x=0$$

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.

$$8x^{2}+6x+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 6 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\times 8\times 5}}{2\times 8}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times 8\times 5}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-6±\sqrt{36-32\times 5}}{2\times 8}$$

Whakareatia -32 ki te 5.

$$x=\frac{-6±\sqrt{36-160}}{2\times 8}$$

Tāpiri 36 ki te -160.

$$x=\frac{-6±\sqrt{-124}}{2\times 8}$$

Tuhia te pūtakerua o te -124.

$$x=\frac{-6±2\sqrt{31}i}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{-6±2\sqrt{31}i}{16}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{31}i}{16} ina he tāpiri te ±. Tāpiri -6 ki te 2i\sqrt{31}.

$$x=\frac{-6+2\sqrt{31}i}{16}$$

Whakawehe -6+2i\sqrt{31} ki te 16.

$$x=\frac{-3+\sqrt{31}i}{8}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{31}i}{16} ina he tango te ±. Tango 2i\sqrt{31} mai i -6.

$$x=\frac{-2\sqrt{31}i-6}{16}$$

Whakawehe -6-2i\sqrt{31} ki te 16.

$$x=\frac{-\sqrt{31}i-3}{8}$$

Kua oti te whārite te whakatau.

$$x=\frac{-3+\sqrt{31}i}{8} x=\frac{-\sqrt{31}i-3}{8}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$8x^{2}+5+6x=0$$

Tangohia te 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$8x^{2}+6x=-5$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}+6x}{8}=-\frac{5}{8}$$

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

$$x^{2}+\frac{6}{8}x=-\frac{5}{8}$$

Whakahekea te hautanga \frac{6}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{3}{4}x=-\frac{5}{8}$$

Whakawehea te \frac{3}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{8}. Nā, tāpiria te pūrua o te \frac{3}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{4}x+\left(\frac{3}{8}\right)^{2}=-\frac{5}{8}+\left(\frac{3}{8}\right)^{2}$$

Pūruatia \frac{3}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=-\frac{5}{8}+\frac{9}{64}$$

Tāpiri -\frac{5}{8} ki te \frac{9}{64} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=-\frac{31}{64}$$

Tauwehea x^{2}+\frac{3}{4}x+\frac{9}{64}. 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}.

$$\left(x+\frac{3}{8}\right)^{2}=-\frac{31}{64}$$

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

$$\sqrt{\left(x+\frac{3}{8}\right)^{2}}=\sqrt{-\frac{31}{64}}$$

Whakarūnātia.

$$x+\frac{3}{8}=\frac{\sqrt{31}i}{8} x+\frac{3}{8}=-\frac{\sqrt{31}i}{8}$$

Me tango \frac{3}{8} mai i ngā taha e rua o te whārite.

$$x=\frac{-3+\sqrt{31}i}{8} x=\frac{-\sqrt{31}i-3}{8}$$