Whakaoti i te x^2+8x+4=-10

$${ x }^{ 2 } +8x+4=-10$$

Whakaoti mō x

$$x=\sqrt{2}-4\approx -2.585786438$$

$$x=-\sqrt{2}-4\approx -5.414213562$$

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.

$$x^{2}+8x+4=-10$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x^{2}+8x+4-\left(-10\right)=-10-\left(-10\right)$$

Mā te tango i te -10 i a ia ake anō ka toe ko te 0.

$$x^{2}+8x+4-\left(-10\right)=0$$

Tango -10 mai i 4.

$$x^{2}+8x+14=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me 14 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 14}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 14}}{2}$$

Whakareatia -4 ki te 14.

$$x=\frac{-8±\sqrt{64-56}}{2}$$

Tāpiri 64 ki te -56.

$$x=\frac{-8±\sqrt{8}}{2}$$

Tuhia te pūtakerua o te 8.

$$x=\frac{-8±2\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{2}.

$$x=\frac{2\sqrt{2}-8}{2}$$

Whakawehe 2\sqrt{2}-8 ki te 2.

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

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{2}}{2} ina he tango te ±. Tango 2\sqrt{2} mai i -8.

$$x=\frac{-2\sqrt{2}-8}{2}$$

Whakawehe -8-2\sqrt{2} ki te 2.

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

Kua oti te whārite te whakatau.

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

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.

$$x^{2}+8x+4=-10$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x^{2}+8x+4-4=-10-4$$

Mā te tango i te 4 i a ia ake anō ka toe ko te 0.

$$x^{2}+8x=-10-4$$

Tango 4 mai i -10.

$$x^{2}+8x=-14$$

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

$$x^{2}+8x+4^{2}=-14+4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=-14+16$$

Tāpiri -14 ki te 16.

$$x^{2}+8x+16=2$$

Tauwehea x^{2}+8x+16. 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}.

$$\left(x+4\right)^{2}=2$$

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

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{2}$$

Whakarūnātia.

$$x+4=\sqrt{2} x+4=-\sqrt{2}$$

Me tango 4 mai i ngā taha e rua o te whārite.

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