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

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

Whakaoti mō x

$$x=\frac{3}{8}=0.375$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -x me -2x, ka -3x.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Pahekotia te 7x^{2} me x^{2}, ka 8x^{2}.

$$8x^{2}-3x=0$$

Tauwehea te x.

$$x\left(8x-3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 8x-3=0.

$$x=0 x=\frac{3}{8}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -x me -2x, ka -3x.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Pahekotia te 7x^{2} me x^{2}, ka 8x^{2}.

$$8x^{2}-3x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -3 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 8}$$

Tuhia te pūtakerua o te \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\times 8}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{3±3}{16}$$

Nā, me whakaoti te whārite x=\frac{3±3}{16} ina he tāpiri te ±. Tāpiri 3 ki te 3.

$$x=\frac{6}{16}$$

Whakahekea te hautanga \frac{6}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{8}$$

Nā, me whakaoti te whārite x=\frac{3±3}{16} ina he tango te ±. Tango 3 mai i 3.

$$x=\frac{0}{16}$$

Whakawehe 0 ki te 16.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{8} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -x me -2x, ka -3x.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Pahekotia te 7x^{2} me x^{2}, ka 8x^{2}.

$$8x^{2}-3x=0$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}-3x}{8}=\frac{0}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$x^{2}-\frac{3}{8}x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x^{2}-\frac{3}{8}x=0$$

Whakawehea te -\frac{3}{8}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{16}. Nā, tāpiria te pūrua o te -\frac{3}{16} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{3}{8}x+\left(-\frac{3}{16}\right)^{2}=\left(-\frac{3}{16}\right)^{2}$$

Pūruatia -\frac{3}{16} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{8}x+\frac{9}{256}=\frac{9}{256}$$

Tauwehea x^{2}-\frac{3}{8}x+\frac{9}{256}. 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}.

$$\left(x-\frac{3}{16}\right)^{2}=\frac{9}{256}$$

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

$$\sqrt{\left(x-\frac{3}{16}\right)^{2}}=\sqrt{\frac{9}{256}}$$

Whakarūnātia.

$$x-\frac{3}{16}=\frac{3}{16} x-\frac{3}{16}=-\frac{3}{16}$$

Me tāpiri \frac{3}{16} ki ngā taha e rua o te whārite.

$$x=\frac{3}{8} x=0$$