Whakaoti i te x^2+4x=2

$$x ^ { 2 } + 4 x = 2$$

Whakaoti mō x (complex solution)

$$x=\sqrt{6}-2\approx 0.449489743$$

$$x=-\left(\sqrt{6}+2\right)\approx -4.449489743$$

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.

$$x^{2}+4x=2$$

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

$$x^{2}+4x-2=2-2$$

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

$$x^{2}+4x-2=0$$

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

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

Pūrua 4.

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

Whakareatia -4 ki te -2.

$$x=\frac{-4±\sqrt{16+8}}{2}$$

Tāpiri 16 ki te 8.

$$x=\frac{-4±\sqrt{24}}{2}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-4±2\sqrt{6}}{2}$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{6}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{6}.

$$x=\frac{2\sqrt{6}-4}{2}$$

Whakawehe -4+2\sqrt{6} ki te 2.

$$x=\sqrt{6}-2$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{6}}{2} ina he tango te ±. Tango 2\sqrt{6} mai i -4.

$$x=\frac{-2\sqrt{6}-4}{2}$$

Whakawehe -4-2\sqrt{6} ki te 2.

$$x=-\sqrt{6}-2$$

Kua oti te whārite te whakatau.

$$x=\sqrt{6}-2 x=-\sqrt{6}-2$$

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.

$$x^{2}+4x=2$$

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

$$x^{2}+4x+2^{2}=2+2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=2+4$$

Tāpiri 2 ki te 4.

$$x^{2}+4x+4=6$$

Tauwehea x^{2}+4x+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}.

$$\left(x+2\right)^{2}=6$$

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{6}$$

Whakarūnātia.

$$x+2=\sqrt{6} x+2=-\sqrt{6}$$

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

$$x=\sqrt{6}-2 x=-\sqrt{6}-2$$

Whakaoti mō x

$$x=\sqrt{6}-2\approx 0.449489743$$

$$x=-\sqrt{6}-2\approx -4.449489743$$

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.

$$x^{2}+4x=2$$

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

$$x^{2}+4x-2=2-2$$

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

$$x^{2}+4x-2=0$$

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

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

Pūrua 4.

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

Whakareatia -4 ki te -2.

$$x=\frac{-4±\sqrt{16+8}}{2}$$

Tāpiri 16 ki te 8.

$$x=\frac{-4±\sqrt{24}}{2}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-4±2\sqrt{6}}{2}$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{6}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{6}.

$$x=\frac{2\sqrt{6}-4}{2}$$

Whakawehe -4+2\sqrt{6} ki te 2.

$$x=\sqrt{6}-2$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{6}}{2} ina he tango te ±. Tango 2\sqrt{6} mai i -4.

$$x=\frac{-2\sqrt{6}-4}{2}$$

Whakawehe -4-2\sqrt{6} ki te 2.

$$x=-\sqrt{6}-2$$

Kua oti te whārite te whakatau.

$$x=\sqrt{6}-2 x=-\sqrt{6}-2$$

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.

$$x^{2}+4x=2$$

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

$$x^{2}+4x+2^{2}=2+2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=2+4$$

Tāpiri 2 ki te 4.

$$x^{2}+4x+4=6$$

Tauwehea x^{2}+4x+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}.

$$\left(x+2\right)^{2}=6$$

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{6}$$

Whakarūnātia.

$$x+2=\sqrt{6} x+2=-\sqrt{6}$$

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

$$x=\sqrt{6}-2 x=-\sqrt{6}-2$$