Whakaoti i te -7x^2-6x=0

$$- 7 x ^ { 2 } - 6 x = 0$$

Whakaoti mō x

$$x=-\frac{6}{7}\approx -0.857142857$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(-7x-6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -7x-6=0.

$$x=0 x=-\frac{6}{7}$$

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.

$$-7x^{2}-6x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -7 mō a, -6 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\left(-7\right)}$$

Tuhia te pūtakerua o te \left(-6\right)^{2}.

$$x=\frac{-\left(-6\right)±6}{2\left(-7\right)}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±6}{2\left(-7\right)}$$

Whakareatia 2 ki te -7.

$$x=\frac{6±6}{-14}$$

Nā, me whakaoti te whārite x=\frac{6±6}{-14} ina he tāpiri te ±. Tāpiri 6 ki te 6.

$$x=\frac{12}{-14}$$

Whakahekea te hautanga \frac{12}{-14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{6}{7}$$

Nā, me whakaoti te whārite x=\frac{6±6}{-14} ina he tango te ±. Tango 6 mai i 6.

$$x=\frac{0}{-14}$$

Whakawehe 0 ki te -14.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{6}{7} x=0$$

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.

$$-7x^{2}-6x=0$$

Whakawehea ngā taha e rua ki te -7.

$$\frac{-7x^{2}-6x}{-7}=\frac{0}{-7}$$

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

$$x^{2}+\left(-\frac{6}{-7}\right)x=\frac{0}{-7}$$

Whakawehe -6 ki te -7.

$$x^{2}+\frac{6}{7}x=\frac{0}{-7}$$

Whakawehe 0 ki te -7.

$$x^{2}+\frac{6}{7}x=0$$

Whakawehea te \frac{6}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{7}. Nā, tāpiria te pūrua o te \frac{3}{7} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{6}{7}x+\left(\frac{3}{7}\right)^{2}=\left(\frac{3}{7}\right)^{2}$$

Pūruatia \frac{3}{7} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{6}{7}x+\frac{9}{49}=\frac{9}{49}$$

Tauwehea x^{2}+\frac{6}{7}x+\frac{9}{49}. 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}.

$$\left(x+\frac{3}{7}\right)^{2}=\frac{9}{49}$$

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

$$\sqrt{\left(x+\frac{3}{7}\right)^{2}}=\sqrt{\frac{9}{49}}$$

Whakarūnātia.

$$x+\frac{3}{7}=\frac{3}{7} x+\frac{3}{7}=-\frac{3}{7}$$

Me tango \frac{3}{7} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{6}{7}$$