Whakaoti i te 7x^2+3x-3=0

$$7 x ^ { 2 } + 3 x - 3 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{93}-3}{14}\approx 0.474546483$$

$$x=\frac{-\sqrt{93}-3}{14}\approx -0.903117911$$

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.

$$7x^{2}+3x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 7 mō a, 3 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times 7\left(-3\right)}}{2\times 7}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 7\left(-3\right)}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$x=\frac{-3±\sqrt{9-28\left(-3\right)}}{2\times 7}$$

Whakareatia -28 ki te -3.

$$x=\frac{-3±\sqrt{9+84}}{2\times 7}$$

Tāpiri 9 ki te 84.

$$x=\frac{-3±\sqrt{93}}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{-3±\sqrt{93}}{14}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{93}}{14} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{93}.

$$x=\frac{\sqrt{93}-3}{14}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{93}}{14} ina he tango te ±. Tango \sqrt{93} mai i -3.

$$x=\frac{-\sqrt{93}-3}{14}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{93}-3}{14} x=\frac{-\sqrt{93}-3}{14}$$

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.

$$7x^{2}+3x-3=0$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$7x^{2}+3x-3-\left(-3\right)=-\left(-3\right)$$

Mā te tango i te -3 i a ia ake anō ka toe ko te 0.

$$7x^{2}+3x=-\left(-3\right)$$

Tango -3 mai i 0.

$$7x^{2}+3x=3$$

Whakawehea ngā taha e rua ki te 7.

$$\frac{7x^{2}+3x}{7}=\frac{3}{7}$$

Mā te whakawehe ki te 7 ka wetekia te whakareanga ki te 7.

$$x^{2}+\frac{3}{7}x=\frac{3}{7}$$

Whakawehea te \frac{3}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{14}. Nā, tāpiria te pūrua o te \frac{3}{14} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{7}x+\left(\frac{3}{14}\right)^{2}=\frac{3}{7}+\left(\frac{3}{14}\right)^{2}$$

Pūruatia \frac{3}{14} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{7}x+\frac{9}{196}=\frac{3}{7}+\frac{9}{196}$$

Tāpiri \frac{3}{7} ki te \frac{9}{196} 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.

$$x^{2}+\frac{3}{7}x+\frac{9}{196}=\frac{93}{196}$$

Tauwehea x^{2}+\frac{3}{7}x+\frac{9}{196}. 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}.

$$\left(x+\frac{3}{14}\right)^{2}=\frac{93}{196}$$

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

$$\sqrt{\left(x+\frac{3}{14}\right)^{2}}=\sqrt{\frac{93}{196}}$$

Whakarūnātia.

$$x+\frac{3}{14}=\frac{\sqrt{93}}{14} x+\frac{3}{14}=-\frac{\sqrt{93}}{14}$$

Me tango \frac{3}{14} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{93}-3}{14} x=\frac{-\sqrt{93}-3}{14}$$