Whakaoti i te x^2+17x-22=0

$$x ^ { 2 } + 17 x - 22 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{377} - 17}{2} \approx 1.208243919$$

$$x=\frac{-\sqrt{377}-17}{2}\approx -18.208243919$$

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.

$$x^{2}+17x-22=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 17 mō b, me -22 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}-4\left(-22\right)}}{2}$$

Pūrua 17.

$$x=\frac{-17±\sqrt{289-4\left(-22\right)}}{2}$$

Whakareatia -4 ki te -22.

$$x=\frac{-17±\sqrt{289+88}}{2}$$

Tāpiri 289 ki te 88.

$$x=\frac{-17±\sqrt{377}}{2}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{377}}{2} ina he tāpiri te ±. Tāpiri -17 ki te \sqrt{377}.

$$x=\frac{\sqrt{377}-17}{2}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{377}}{2} ina he tango te ±. Tango \sqrt{377} mai i -17.

$$x=\frac{-\sqrt{377}-17}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{377}-17}{2} x=\frac{-\sqrt{377}-17}{2}$$

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.

$$x^{2}+17x-22=0$$

Me tāpiri 22 ki ngā taha e rua o te whārite.

$$x^{2}+17x-22-\left(-22\right)=-\left(-22\right)$$

Mā te tango i te -22 i a ia ake anō ka toe ko te 0.

$$x^{2}+17x=-\left(-22\right)$$

Tango -22 mai i 0.

$$x^{2}+17x=22$$

Whakawehea te 17, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{17}{2}. Nā, tāpiria te pūrua o te \frac{17}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+17x+\left(\frac{17}{2}\right)^{2}=22+\left(\frac{17}{2}\right)^{2}$$

Pūruatia \frac{17}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+17x+\frac{289}{4}=22+\frac{289}{4}$$

Tāpiri 22 ki te \frac{289}{4}.

$$x^{2}+17x+\frac{289}{4}=\frac{377}{4}$$

Tauwehea x^{2}+17x+\frac{289}{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}.

$$\left(x+\frac{17}{2}\right)^{2}=\frac{377}{4}$$

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

$$\sqrt{\left(x+\frac{17}{2}\right)^{2}}=\sqrt{\frac{377}{4}}$$

Whakarūnātia.

$$x+\frac{17}{2}=\frac{\sqrt{377}}{2} x+\frac{17}{2}=-\frac{\sqrt{377}}{2}$$

Me tango \frac{17}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{377}-17}{2} x=\frac{-\sqrt{377}-17}{2}$$