Whakaoti i te 101x^2+7x+6=0

$$101 x ^ { 2 } + 7 x + 6 = 0$$

Whakaoti mō x (complex solution)

$$x=\frac{-7+5\sqrt{95}i}{202}\approx -0.034653465+0.241257286i$$

$$x=\frac{-5\sqrt{95}i-7}{202}\approx -0.034653465-0.241257286i$$

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.

$$101x^{2}+7x+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 101 mō a, 7 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\times 101\times 6}}{2\times 101}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\times 101\times 6}}{2\times 101}$$

Whakareatia -4 ki te 101.

$$x=\frac{-7±\sqrt{49-404\times 6}}{2\times 101}$$

Whakareatia -404 ki te 6.

$$x=\frac{-7±\sqrt{49-2424}}{2\times 101}$$

Tāpiri 49 ki te -2424.

$$x=\frac{-7±\sqrt{-2375}}{2\times 101}$$

Tuhia te pūtakerua o te -2375.

$$x=\frac{-7±5\sqrt{95}i}{2\times 101}$$

Whakareatia 2 ki te 101.

$$x=\frac{-7±5\sqrt{95}i}{202}$$

Nā, me whakaoti te whārite x=\frac{-7±5\sqrt{95}i}{202} ina he tāpiri te ±. Tāpiri -7 ki te 5i\sqrt{95}.

$$x=\frac{-7+5\sqrt{95}i}{202}$$

Nā, me whakaoti te whārite x=\frac{-7±5\sqrt{95}i}{202} ina he tango te ±. Tango 5i\sqrt{95} mai i -7.

$$x=\frac{-5\sqrt{95}i-7}{202}$$

Kua oti te whārite te whakatau.

$$x=\frac{-7+5\sqrt{95}i}{202} x=\frac{-5\sqrt{95}i-7}{202}$$

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.

$$101x^{2}+7x+6=0$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$101x^{2}+7x+6-6=-6$$

Mā te tango i te 6 i a ia ake anō ka toe ko te 0.

$$101x^{2}+7x=-6$$

Whakawehea ngā taha e rua ki te 101.

$$\frac{101x^{2}+7x}{101}=-\frac{6}{101}$$

Mā te whakawehe ki te 101 ka wetekia te whakareanga ki te 101.

$$x^{2}+\frac{7}{101}x=-\frac{6}{101}$$

Whakawehea te \frac{7}{101}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{202}. Nā, tāpiria te pūrua o te \frac{7}{202} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{7}{101}x+\left(\frac{7}{202}\right)^{2}=-\frac{6}{101}+\left(\frac{7}{202}\right)^{2}$$

Pūruatia \frac{7}{202} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{7}{101}x+\frac{49}{40804}=-\frac{6}{101}+\frac{49}{40804}$$

Tāpiri -\frac{6}{101} ki te \frac{49}{40804} 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.

$$x^{2}+\frac{7}{101}x+\frac{49}{40804}=-\frac{2375}{40804}$$

Tauwehea x^{2}+\frac{7}{101}x+\frac{49}{40804}. 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}.

$$\left(x+\frac{7}{202}\right)^{2}=-\frac{2375}{40804}$$

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

$$\sqrt{\left(x+\frac{7}{202}\right)^{2}}=\sqrt{-\frac{2375}{40804}}$$

Whakarūnātia.

$$x+\frac{7}{202}=\frac{5\sqrt{95}i}{202} x+\frac{7}{202}=-\frac{5\sqrt{95}i}{202}$$

Me tango \frac{7}{202} mai i ngā taha e rua o te whārite.

$$x=\frac{-7+5\sqrt{95}i}{202} x=\frac{-5\sqrt{95}i-7}{202}$$