Whakaoti i te -18a^2-34a-4=0

$$- 18 a ^ { 2 } - 34 a - 4 = 0$$

Whakaoti mō a

$$a=\frac{\sqrt{217}-17}{18}\approx -0.126060008$$

$$a=\frac{-\sqrt{217}-17}{18}\approx -1.762828881$$

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.

$$-18a^{2}-34a-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -18 mō a, -34 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-34\right)±\sqrt{\left(-34\right)^{2}-4\left(-18\right)\left(-4\right)}}{2\left(-18\right)}$$

Pūrua -34.

$$a=\frac{-\left(-34\right)±\sqrt{1156-4\left(-18\right)\left(-4\right)}}{2\left(-18\right)}$$

Whakareatia -4 ki te -18.

$$a=\frac{-\left(-34\right)±\sqrt{1156+72\left(-4\right)}}{2\left(-18\right)}$$

Whakareatia 72 ki te -4.

$$a=\frac{-\left(-34\right)±\sqrt{1156-288}}{2\left(-18\right)}$$

Tāpiri 1156 ki te -288.

$$a=\frac{-\left(-34\right)±\sqrt{868}}{2\left(-18\right)}$$

Tuhia te pūtakerua o te 868.

$$a=\frac{-\left(-34\right)±2\sqrt{217}}{2\left(-18\right)}$$

Ko te tauaro o -34 ko 34.

$$a=\frac{34±2\sqrt{217}}{2\left(-18\right)}$$

Whakareatia 2 ki te -18.

$$a=\frac{34±2\sqrt{217}}{-36}$$

Nā, me whakaoti te whārite a=\frac{34±2\sqrt{217}}{-36} ina he tāpiri te ±. Tāpiri 34 ki te 2\sqrt{217}.

$$a=\frac{2\sqrt{217}+34}{-36}$$

Whakawehe 34+2\sqrt{217} ki te -36.

$$a=\frac{-\sqrt{217}-17}{18}$$

Nā, me whakaoti te whārite a=\frac{34±2\sqrt{217}}{-36} ina he tango te ±. Tango 2\sqrt{217} mai i 34.

$$a=\frac{34-2\sqrt{217}}{-36}$$

Whakawehe 34-2\sqrt{217} ki te -36.

$$a=\frac{\sqrt{217}-17}{18}$$

Kua oti te whārite te whakatau.

$$a=\frac{-\sqrt{217}-17}{18} a=\frac{\sqrt{217}-17}{18}$$

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.

$$-18a^{2}-34a-4=0$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$-18a^{2}-34a-4-\left(-4\right)=-\left(-4\right)$$

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

$$-18a^{2}-34a=-\left(-4\right)$$

Tango -4 mai i 0.

$$-18a^{2}-34a=4$$

Whakawehea ngā taha e rua ki te -18.

$$\frac{-18a^{2}-34a}{-18}=\frac{4}{-18}$$

Mā te whakawehe ki te -18 ka wetekia te whakareanga ki te -18.

$$a^{2}+\left(-\frac{34}{-18}\right)a=\frac{4}{-18}$$

Whakahekea te hautanga \frac{-34}{-18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a^{2}+\frac{17}{9}a=\frac{4}{-18}$$

Whakahekea te hautanga \frac{4}{-18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a^{2}+\frac{17}{9}a=-\frac{2}{9}$$

Whakawehea te \frac{17}{9}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{17}{18}. Nā, tāpiria te pūrua o te \frac{17}{18} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+\frac{17}{9}a+\left(\frac{17}{18}\right)^{2}=-\frac{2}{9}+\left(\frac{17}{18}\right)^{2}$$

Pūruatia \frac{17}{18} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}+\frac{17}{9}a+\frac{289}{324}=-\frac{2}{9}+\frac{289}{324}$$

Tāpiri -\frac{2}{9} ki te \frac{289}{324} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$a^{2}+\frac{17}{9}a+\frac{289}{324}=\frac{217}{324}$$

Tauwehea a^{2}+\frac{17}{9}a+\frac{289}{324}. 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}.

$$\left(a+\frac{17}{18}\right)^{2}=\frac{217}{324}$$

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

$$\sqrt{\left(a+\frac{17}{18}\right)^{2}}=\sqrt{\frac{217}{324}}$$

Whakarūnātia.

$$a+\frac{17}{18}=\frac{\sqrt{217}}{18} a+\frac{17}{18}=-\frac{\sqrt{217}}{18}$$

Me tango \frac{17}{18} mai i ngā taha e rua o te whārite.

$$a=\frac{\sqrt{217}-17}{18} a=\frac{-\sqrt{217}-17}{18}$$