Whakaoti i te 7x^2=4x

$$7 x ^ { 2 } = 4 x$$

Whakaoti mō x

$$x=\frac{4}{7}\approx 0.571428571$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 4x mai i ngā taha e rua.

$$7x^{2}-4x=0$$

Tauwehea te x.

$$x\left(7x-4\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 7x-4=0.

$$x=0 x=\frac{4}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 4x mai i ngā taha e rua.

$$7x^{2}-4x=0$$

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

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

Tuhia te pūtakerua o te \left(-4\right)^{2}.

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

Ko te tauaro o -4 ko 4.

$$x=\frac{4±4}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{4±4}{14}$$

Nā, me whakaoti te whārite x=\frac{4±4}{14} ina he tāpiri te ±. Tāpiri 4 ki te 4.

$$x=\frac{8}{14}$$

Whakahekea te hautanga \frac{8}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{4}{7}$$

Nā, me whakaoti te whārite x=\frac{4±4}{14} ina he tango te ±. Tango 4 mai i 4.

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

Whakawehe 0 ki te 14.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{4}{7} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 4x mai i ngā taha e rua.

$$7x^{2}-4x=0$$

Whakawehea ngā taha e rua ki te 7.

$$\frac{7x^{2}-4x}{7}=\frac{0}{7}$$

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

$$x^{2}-\frac{4}{7}x=\frac{0}{7}$$

Whakawehe 0 ki te 7.

$$x^{2}-\frac{4}{7}x=0$$

Whakawehea te -\frac{4}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{2}{7}. Nā, tāpiria te pūrua o te -\frac{2}{7} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{4}{7}x+\left(-\frac{2}{7}\right)^{2}=\left(-\frac{2}{7}\right)^{2}$$

Pūruatia -\frac{2}{7} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{4}{7}x+\frac{4}{49}=\frac{4}{49}$$

Tauwehea x^{2}-\frac{4}{7}x+\frac{4}{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}.

$$\left(x-\frac{2}{7}\right)^{2}=\frac{4}{49}$$

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

$$\sqrt{\left(x-\frac{2}{7}\right)^{2}}=\sqrt{\frac{4}{49}}$$

Whakarūnātia.

$$x-\frac{2}{7}=\frac{2}{7} x-\frac{2}{7}=-\frac{2}{7}$$

Me tāpiri \frac{2}{7} ki ngā taha e rua o te whārite.

$$x=\frac{4}{7} x=0$$