Whakaoti i te 42x^2+13x-35=0

$$42 x ^ { 2 } + 13 x - 35 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{6049}-13}{84}\approx 0.771134731$$

$$x=\frac{-\sqrt{6049}-13}{84}\approx -1.080658541$$

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.

$$42x^{2}+13x-35=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 42 mō a, 13 mō b, me -35 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-13±\sqrt{13^{2}-4\times 42\left(-35\right)}}{2\times 42}$$

Pūrua 13.

$$x=\frac{-13±\sqrt{169-4\times 42\left(-35\right)}}{2\times 42}$$

Whakareatia -4 ki te 42.

$$x=\frac{-13±\sqrt{169-168\left(-35\right)}}{2\times 42}$$

Whakareatia -168 ki te -35.

$$x=\frac{-13±\sqrt{169+5880}}{2\times 42}$$

Tāpiri 169 ki te 5880.

$$x=\frac{-13±\sqrt{6049}}{2\times 42}$$

Whakareatia 2 ki te 42.

$$x=\frac{-13±\sqrt{6049}}{84}$$

Nā, me whakaoti te whārite x=\frac{-13±\sqrt{6049}}{84} ina he tāpiri te ±. Tāpiri -13 ki te \sqrt{6049}.

$$x=\frac{\sqrt{6049}-13}{84}$$

Nā, me whakaoti te whārite x=\frac{-13±\sqrt{6049}}{84} ina he tango te ±. Tango \sqrt{6049} mai i -13.

$$x=\frac{-\sqrt{6049}-13}{84}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{6049}-13}{84} x=\frac{-\sqrt{6049}-13}{84}$$

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.

$$42x^{2}+13x-35=0$$

Me tāpiri 35 ki ngā taha e rua o te whārite.

$$42x^{2}+13x-35-\left(-35\right)=-\left(-35\right)$$

Mā te tango i te -35 i a ia ake anō ka toe ko te 0.

$$42x^{2}+13x=-\left(-35\right)$$

Tango -35 mai i 0.

$$42x^{2}+13x=35$$

Whakawehea ngā taha e rua ki te 42.

$$\frac{42x^{2}+13x}{42}=\frac{35}{42}$$

Mā te whakawehe ki te 42 ka wetekia te whakareanga ki te 42.

$$x^{2}+\frac{13}{42}x=\frac{35}{42}$$

Whakahekea te hautanga \frac{35}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$x^{2}+\frac{13}{42}x=\frac{5}{6}$$

Whakawehea te \frac{13}{42}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{13}{84}. Nā, tāpiria te pūrua o te \frac{13}{84} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{13}{42}x+\left(\frac{13}{84}\right)^{2}=\frac{5}{6}+\left(\frac{13}{84}\right)^{2}$$

Pūruatia \frac{13}{84} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{13}{42}x+\frac{169}{7056}=\frac{5}{6}+\frac{169}{7056}$$

Tāpiri \frac{5}{6} ki te \frac{169}{7056} 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.

$$x^{2}+\frac{13}{42}x+\frac{169}{7056}=\frac{6049}{7056}$$

Tauwehea x^{2}+\frac{13}{42}x+\frac{169}{7056}. 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}.

$$\left(x+\frac{13}{84}\right)^{2}=\frac{6049}{7056}$$

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

$$\sqrt{\left(x+\frac{13}{84}\right)^{2}}=\sqrt{\frac{6049}{7056}}$$

Whakarūnātia.

$$x+\frac{13}{84}=\frac{\sqrt{6049}}{84} x+\frac{13}{84}=-\frac{\sqrt{6049}}{84}$$

Me tango \frac{13}{84} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{6049}-13}{84} x=\frac{-\sqrt{6049}-13}{84}$$