Whakaoti i te 88x^2-16x=-36

$$88 { x }^{ 2 } -16x=-36$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{194}i}{22}+\frac{1}{11}\approx 0.090909091+0.633108558i$$

$$x=-\frac{\sqrt{194}i}{22}+\frac{1}{11}\approx 0.090909091-0.633108558i$$

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.

$$88x^{2}-16x=-36$$

Me tāpiri 36 ki ngā taha e rua o te whārite.

$$88x^{2}-16x-\left(-36\right)=-36-\left(-36\right)$$

Mā te tango i te -36 i a ia ake anō ka toe ko te 0.

$$88x^{2}-16x-\left(-36\right)=0$$

Tango -36 mai i 0.

$$88x^{2}-16x+36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 88 mō a, -16 mō b, me 36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 88\times 36}}{2\times 88}$$

Pūrua -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\times 88\times 36}}{2\times 88}$$

Whakareatia -4 ki te 88.

$$x=\frac{-\left(-16\right)±\sqrt{256-352\times 36}}{2\times 88}$$

Whakareatia -352 ki te 36.

$$x=\frac{-\left(-16\right)±\sqrt{256-12672}}{2\times 88}$$

Tāpiri 256 ki te -12672.

$$x=\frac{-\left(-16\right)±\sqrt{-12416}}{2\times 88}$$

Tuhia te pūtakerua o te -12416.

$$x=\frac{-\left(-16\right)±8\sqrt{194}i}{2\times 88}$$

Ko te tauaro o -16 ko 16.

$$x=\frac{16±8\sqrt{194}i}{2\times 88}$$

Whakareatia 2 ki te 88.

$$x=\frac{16±8\sqrt{194}i}{176}$$

Nā, me whakaoti te whārite x=\frac{16±8\sqrt{194}i}{176} ina he tāpiri te ±. Tāpiri 16 ki te 8i\sqrt{194}.

$$x=\frac{16+8\sqrt{194}i}{176}$$

Whakawehe 16+8i\sqrt{194} ki te 176.

$$x=\frac{\sqrt{194}i}{22}+\frac{1}{11}$$

Nā, me whakaoti te whārite x=\frac{16±8\sqrt{194}i}{176} ina he tango te ±. Tango 8i\sqrt{194} mai i 16.

$$x=\frac{-8\sqrt{194}i+16}{176}$$

Whakawehe 16-8i\sqrt{194} ki te 176.

$$x=-\frac{\sqrt{194}i}{22}+\frac{1}{11}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{194}i}{22}+\frac{1}{11} x=-\frac{\sqrt{194}i}{22}+\frac{1}{11}$$

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.

$$88x^{2}-16x=-36$$

Whakawehea ngā taha e rua ki te 88.

$$\frac{88x^{2}-16x}{88}=-\frac{36}{88}$$

Mā te whakawehe ki te 88 ka wetekia te whakareanga ki te 88.

$$x^{2}+\left(-\frac{16}{88}\right)x=-\frac{36}{88}$$

Whakahekea te hautanga \frac{-16}{88} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x^{2}-\frac{2}{11}x=-\frac{36}{88}$$

Whakahekea te hautanga \frac{-36}{88} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{2}{11}x=-\frac{9}{22}$$

Whakawehea te -\frac{2}{11}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{11}. Nā, tāpiria te pūrua o te -\frac{1}{11} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{2}{11}x+\left(-\frac{1}{11}\right)^{2}=-\frac{9}{22}+\left(-\frac{1}{11}\right)^{2}$$

Pūruatia -\frac{1}{11} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{2}{11}x+\frac{1}{121}=-\frac{9}{22}+\frac{1}{121}$$

Tāpiri -\frac{9}{22} ki te \frac{1}{121} 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.

$$x^{2}-\frac{2}{11}x+\frac{1}{121}=-\frac{97}{242}$$

Tauwehea x^{2}-\frac{2}{11}x+\frac{1}{121}. 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}.

$$\left(x-\frac{1}{11}\right)^{2}=-\frac{97}{242}$$

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

$$\sqrt{\left(x-\frac{1}{11}\right)^{2}}=\sqrt{-\frac{97}{242}}$$

Whakarūnātia.

$$x-\frac{1}{11}=\frac{\sqrt{194}i}{22} x-\frac{1}{11}=-\frac{\sqrt{194}i}{22}$$

Me tāpiri \frac{1}{11} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{194}i}{22}+\frac{1}{11} x=-\frac{\sqrt{194}i}{22}+\frac{1}{11}$$