Whakaoti i te 4w^2=7w

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

Whakaoti mō w

$$w = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

$$w=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 7w mai i ngā taha e rua.

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

Tauwehea te w.

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

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7w mai i ngā taha e rua.

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

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

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

Tuhia te pūtakerua o te \left(-7\right)^{2}.

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

Ko te tauaro o -7 ko 7.

$$w=\frac{7±7}{2\times 4}$$

Whakareatia 2 ki te 4.

$$w=\frac{7±7}{8}$$

Nā, me whakaoti te whārite w=\frac{7±7}{8} ina he tāpiri te ±. Tāpiri 7 ki te 7.

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

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

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

Nā, me whakaoti te whārite w=\frac{7±7}{8} ina he tango te ±. Tango 7 mai i 7.

$$w=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$w=0$$

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 7w mai i ngā taha e rua.

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

Whakawehea ngā taha e rua ki te 4.

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

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

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

Whakawehe 0 ki te 4.

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

Whakawehea te -\frac{7}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{8}. Nā, tāpiria te pūrua o te -\frac{7}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$w^{2}-\frac{7}{4}w+\left(-\frac{7}{8}\right)^{2}=\left(-\frac{7}{8}\right)^{2}$$

Pūruatia -\frac{7}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$w^{2}-\frac{7}{4}w+\frac{49}{64}=\frac{49}{64}$$

Tauwehea w^{2}-\frac{7}{4}w+\frac{49}{64}. 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}.

$$\left(w-\frac{7}{8}\right)^{2}=\frac{49}{64}$$

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

$$\sqrt{\left(w-\frac{7}{8}\right)^{2}}=\sqrt{\frac{49}{64}}$$

Whakarūnātia.

$$w-\frac{7}{8}=\frac{7}{8} w-\frac{7}{8}=-\frac{7}{8}$$

Me tāpiri \frac{7}{8} ki ngā taha e rua o te whārite.

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