Whakaoti i te 4x^2=12-3x

$$4 x ^ { 2 } = 12 - 3 x$$

Whakaoti mō x

$$x = \frac{\sqrt{201} - 3}{8} \approx 1.39718086$$

$$x=\frac{-\sqrt{201}-3}{8}\approx -2.14718086$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 12 mai i ngā taha e rua.

$$4x^{2}-12=-3x$$

Me tāpiri te 3x ki ngā taha e rua.

$$4x^{2}-12+3x=0$$

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.

$$4x^{2}+3x-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 3 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times 4\left(-12\right)}}{2\times 4}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 4\left(-12\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-3±\sqrt{9-16\left(-12\right)}}{2\times 4}$$

Whakareatia -16 ki te -12.

$$x=\frac{-3±\sqrt{9+192}}{2\times 4}$$

Tāpiri 9 ki te 192.

$$x=\frac{-3±\sqrt{201}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-3±\sqrt{201}}{8}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{201}}{8} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{201}.

$$x=\frac{\sqrt{201}-3}{8}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{201}}{8} ina he tango te ±. Tango \sqrt{201} mai i -3.

$$x=\frac{-\sqrt{201}-3}{8}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{201}-3}{8} x=\frac{-\sqrt{201}-3}{8}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 3x ki ngā taha e rua.

$$4x^{2}+3x=12$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+3x}{4}=\frac{12}{4}$$

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

$$x^{2}+\frac{3}{4}x=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$x^{2}+\frac{3}{4}x=3$$

Whakawehea te \frac{3}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{8}. Nā, tāpiria te pūrua o te \frac{3}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{4}x+\left(\frac{3}{8}\right)^{2}=3+\left(\frac{3}{8}\right)^{2}$$

Pūruatia \frac{3}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=3+\frac{9}{64}$$

Tāpiri 3 ki te \frac{9}{64}.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=\frac{201}{64}$$

Tauwehea te x^{2}+\frac{3}{4}x+\frac{9}{64}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{8}\right)^{2}=\frac{201}{64}$$

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

$$\sqrt{\left(x+\frac{3}{8}\right)^{2}}=\sqrt{\frac{201}{64}}$$

Whakarūnātia.

$$x+\frac{3}{8}=\frac{\sqrt{201}}{8} x+\frac{3}{8}=-\frac{\sqrt{201}}{8}$$

Me tango \frac{3}{8} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{201}-3}{8} x=\frac{-\sqrt{201}-3}{8}$$