Whakaoti i te 2x^2=-35x-1

$$2 x ^ { 2 } = - 35 x - 1$$

Whakaoti mō x

$$x=\frac{\sqrt{1217}-35}{4}\approx -0.028618229$$

$$x=\frac{-\sqrt{1217}-35}{4}\approx -17.471381771$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 35x ki ngā taha e rua.

$$2x^{2}+35x=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$2x^{2}+35x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 35 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-35±\sqrt{35^{2}-4\times 2}}{2\times 2}$$

Pūrua 35.

$$x=\frac{-35±\sqrt{1225-4\times 2}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-35±\sqrt{1225-8}}{2\times 2}$$

Tāpiri 1225 ki te -8.

$$x=\frac{-35±\sqrt{1217}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-35±\sqrt{1217}}{4}$$

Nā, me whakaoti te whārite x=\frac{-35±\sqrt{1217}}{4} ina he tāpiri te ±. Tāpiri -35 ki te \sqrt{1217}.

$$x=\frac{\sqrt{1217}-35}{4}$$

Nā, me whakaoti te whārite x=\frac{-35±\sqrt{1217}}{4} ina he tango te ±. Tango \sqrt{1217} mai i -35.

$$x=\frac{-\sqrt{1217}-35}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{1217}-35}{4} x=\frac{-\sqrt{1217}-35}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 35x ki ngā taha e rua.

$$2x^{2}+35x=-1$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+35x}{2}=-\frac{1}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{35}{2}x=-\frac{1}{2}$$

Whakawehea te \frac{35}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{35}{4}. Nā, tāpiria te pūrua o te \frac{35}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{35}{2}x+\left(\frac{35}{4}\right)^{2}=-\frac{1}{2}+\left(\frac{35}{4}\right)^{2}$$

Pūruatia \frac{35}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{35}{2}x+\frac{1225}{16}=-\frac{1}{2}+\frac{1225}{16}$$

Tāpiri -\frac{1}{2} ki te \frac{1225}{16} 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.

$$x^{2}+\frac{35}{2}x+\frac{1225}{16}=\frac{1217}{16}$$

Tauwehea x^{2}+\frac{35}{2}x+\frac{1225}{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}.

$$\left(x+\frac{35}{4}\right)^{2}=\frac{1217}{16}$$

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

$$\sqrt{\left(x+\frac{35}{4}\right)^{2}}=\sqrt{\frac{1217}{16}}$$

Whakarūnātia.

$$x+\frac{35}{4}=\frac{\sqrt{1217}}{4} x+\frac{35}{4}=-\frac{\sqrt{1217}}{4}$$

Me tango \frac{35}{4} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{1217}-35}{4} x=\frac{-\sqrt{1217}-35}{4}$$