Whakaoti i te x^2+7x-12=0

$$x ^ { 2 } + 7 x - 12 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{97} - 7}{2} \approx 1.424428901$$

$$x=\frac{-\sqrt{97}-7}{2}\approx -8.424428901$$

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.

$$x^{2}+7x-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-12\right)}}{2}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\left(-12\right)}}{2}$$

Whakareatia -4 ki te -12.

$$x=\frac{-7±\sqrt{49+48}}{2}$$

Tāpiri 49 ki te 48.

$$x=\frac{-7±\sqrt{97}}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{97}}{2} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{97}.

$$x=\frac{\sqrt{97}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{97}}{2} ina he tango te ±. Tango \sqrt{97} mai i -7.

$$x=\frac{-\sqrt{97}-7}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$

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.

$$x^{2}+7x-12=0$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$x^{2}+7x-12-\left(-12\right)=-\left(-12\right)$$

Mā te tango i te -12 i a ia ake anō ka toe ko te 0.

$$x^{2}+7x=-\left(-12\right)$$

Tango -12 mai i 0.

$$x^{2}+7x=12$$

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

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=12+\left(\frac{7}{2}\right)^{2}$$

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+7x+\frac{49}{4}=12+\frac{49}{4}$$

Tāpiri 12 ki te \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{97}{4}$$

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

$$\left(x+\frac{7}{2}\right)^{2}=\frac{97}{4}$$

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

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{97}{4}}$$

Whakarūnātia.

$$x+\frac{7}{2}=\frac{\sqrt{97}}{2} x+\frac{7}{2}=-\frac{\sqrt{97}}{2}$$

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$