Whakaoti i te 44+x^2-x=2

$$44+ { x }^{ 2 } -x=2$$

Whakaoti mō x (complex solution)

$$x=\frac{1+\sqrt{167}i}{2}\approx 0.5+6.461423992i$$

$$x=\frac{-\sqrt{167}i+1}{2}\approx 0.5-6.461423992i$$

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.

$$x^{2}-x+44=2$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x^{2}-x+44-2=2-2$$

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

$$x^{2}-x+44-2=0$$

Tango 2 mai i 44.

$$x^{2}-x+42=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -1 mō b, me 42 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 42}}{2}$$

Whakareatia -4 ki te 42.

$$x=\frac{-\left(-1\right)±\sqrt{1-168}}{2}$$

Tāpiri 1 ki te -168.

$$x=\frac{-\left(-1\right)±\sqrt{-167}}{2}$$

Tuhia te pūtakerua o te -167.

$$x=\frac{-\left(-1\right)±\sqrt{167}i}{2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{167}i}{2}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{167}i}{2} ina he tāpiri te ±. Tāpiri 1 ki te i\sqrt{167}.

$$x=\frac{1+\sqrt{167}i}{2}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{167}i}{2} ina he tango te ±. Tango i\sqrt{167} mai i 1.

$$x=\frac{-\sqrt{167}i+1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{1+\sqrt{167}i}{2} x=\frac{-\sqrt{167}i+1}{2}$$

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.

$$x^{2}-x+44=2$$

Me tango 44 mai i ngā taha e rua o te whārite.

$$x^{2}-x+44-44=2-44$$

Mā te tango i te 44 i a ia ake anō ka toe ko te 0.

$$x^{2}-x=2-44$$

Tango 44 mai i 2.

$$x^{2}-x=-42$$

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

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-42+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-x+\frac{1}{4}=-42+\frac{1}{4}$$

Tāpiri -42 ki te \frac{1}{4}.

$$x^{2}-x+\frac{1}{4}=-\frac{167}{4}$$

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

$$\left(x-\frac{1}{2}\right)^{2}=-\frac{167}{4}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{167}{4}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{\sqrt{167}i}{2} x-\frac{1}{2}=-\frac{\sqrt{167}i}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$x=\frac{1+\sqrt{167}i}{2} x=\frac{-\sqrt{167}i+1}{2}$$