Whakaoti i te 4x*2x+3x=72

$$4x \times 2x+3x=72$$

Whakaoti mō x

$$x = \frac{3 \sqrt{257} - 3}{16} \approx 2.818353664$$

$$x=\frac{-3\sqrt{257}-3}{16}\approx -3.193353664$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$4x^{2}\times 2+3x=72$$

Whakareatia te 4 ki te 2, ka 8.

$$8x^{2}+3x=72$$

Tangohia te 72 mai i ngā taha e rua.

$$8x^{2}+3x-72=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 3 mō b, me -72 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times 8\left(-72\right)}}{2\times 8}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 8\left(-72\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-3±\sqrt{9-32\left(-72\right)}}{2\times 8}$$

Whakareatia -32 ki te -72.

$$x=\frac{-3±\sqrt{9+2304}}{2\times 8}$$

Tāpiri 9 ki te 2304.

$$x=\frac{-3±\sqrt{2313}}{2\times 8}$$

Tuhia te pūtakerua o te 2313.

$$x=\frac{-3±3\sqrt{257}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{-3±3\sqrt{257}}{16}$$

Nā, me whakaoti te whārite x=\frac{-3±3\sqrt{257}}{16} ina he tāpiri te ±. Tāpiri -3 ki te 3\sqrt{257}.

$$x=\frac{3\sqrt{257}-3}{16}$$

Nā, me whakaoti te whārite x=\frac{-3±3\sqrt{257}}{16} ina he tango te ±. Tango 3\sqrt{257} mai i -3.

$$x=\frac{-3\sqrt{257}-3}{16}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{257}-3}{16} x=\frac{-3\sqrt{257}-3}{16}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$4x^{2}\times 2+3x=72$$

Whakareatia te 4 ki te 2, ka 8.

$$8x^{2}+3x=72$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}+3x}{8}=\frac{72}{8}$$

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

$$x^{2}+\frac{3}{8}x=\frac{72}{8}$$

Whakawehe 72 ki te 8.

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

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.

$$x^{2}+\frac{3}{8}x+\left(\frac{3}{16}\right)^{2}=9+\left(\frac{3}{16}\right)^{2}$$

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

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

Tāpiri 9 ki te \frac{9}{256}.

$$x^{2}+\frac{3}{8}x+\frac{9}{256}=\frac{2313}{256}$$

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}.

$$\left(x+\frac{3}{16}\right)^{2}=\frac{2313}{256}$$

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

$$\sqrt{\left(x+\frac{3}{16}\right)^{2}}=\sqrt{\frac{2313}{256}}$$

Whakarūnātia.

$$x+\frac{3}{16}=\frac{3\sqrt{257}}{16} x+\frac{3}{16}=-\frac{3\sqrt{257}}{16}$$

Me tango \frac{3}{16} mai i ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{257}-3}{16} x=\frac{-3\sqrt{257}-3}{16}$$