Whakaoti i te 6x*2x+4=2x+2*2x+12

$$6x \times 2x+4=2x+2 \times 2x+12$$

Whakaoti mō x

$$x=\frac{\sqrt{105}}{12}+\frac{1}{4}\approx 1.103912564$$

$$x=-\frac{\sqrt{105}}{12}+\frac{1}{4}\approx -0.603912564$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$6x^{2}\times 2+4=2x+2\times 2x+12$$

Whakareatia te 6 ki te 2, ka 12.

$$12x^{2}+4=2x+2\times 2x+12$$

Whakareatia te 2 ki te 2, ka 4.

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

Pahekotia te 2x me 4x, ka 6x.

$$12x^{2}+4=6x+12$$

Tangohia te 6x mai i ngā taha e rua.

$$12x^{2}+4-6x=12$$

Tangohia te 12 mai i ngā taha e rua.

$$12x^{2}+4-6x-12=0$$

Tangohia te 12 i te 4, ka -8.

$$12x^{2}-8-6x=0$$

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.

$$12x^{2}-6x-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, -6 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 12\left(-8\right)}}{2\times 12}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 12\left(-8\right)}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$x=\frac{-\left(-6\right)±\sqrt{36-48\left(-8\right)}}{2\times 12}$$

Whakareatia -48 ki te -8.

$$x=\frac{-\left(-6\right)±\sqrt{36+384}}{2\times 12}$$

Tāpiri 36 ki te 384.

$$x=\frac{-\left(-6\right)±\sqrt{420}}{2\times 12}$$

Tuhia te pūtakerua o te 420.

$$x=\frac{-\left(-6\right)±2\sqrt{105}}{2\times 12}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{105}}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{6±2\sqrt{105}}{24}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{105}}{24} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{105}.

$$x=\frac{2\sqrt{105}+6}{24}$$

Whakawehe 6+2\sqrt{105} ki te 24.

$$x=\frac{\sqrt{105}}{12}+\frac{1}{4}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{105}}{24} ina he tango te ±. Tango 2\sqrt{105} mai i 6.

$$x=\frac{6-2\sqrt{105}}{24}$$

Whakawehe 6-2\sqrt{105} ki te 24.

$$x=-\frac{\sqrt{105}}{12}+\frac{1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{105}}{12}+\frac{1}{4} x=-\frac{\sqrt{105}}{12}+\frac{1}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$6x^{2}\times 2+4=2x+2\times 2x+12$$

Whakareatia te 6 ki te 2, ka 12.

$$12x^{2}+4=2x+2\times 2x+12$$

Whakareatia te 2 ki te 2, ka 4.

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

Pahekotia te 2x me 4x, ka 6x.

$$12x^{2}+4=6x+12$$

Tangohia te 6x mai i ngā taha e rua.

$$12x^{2}+4-6x=12$$

Tangohia te 4 mai i ngā taha e rua.

$$12x^{2}-6x=12-4$$

Tangohia te 4 i te 12, ka 8.

$$12x^{2}-6x=8$$

Whakawehea ngā taha e rua ki te 12.

$$\frac{12x^{2}-6x}{12}=\frac{8}{12}$$

Mā te whakawehe ki te 12 ka wetekia te whakareanga ki te 12.

$$x^{2}+\left(-\frac{6}{12}\right)x=\frac{8}{12}$$

Whakahekea te hautanga \frac{-6}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x^{2}-\frac{1}{2}x=\frac{8}{12}$$

Whakahekea te hautanga \frac{8}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{1}{2}x=\frac{2}{3}$$

Whakawehea te -\frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4}. Nā, tāpiria te pūrua o te -\frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=\frac{2}{3}+\left(-\frac{1}{4}\right)^{2}$$

Pūruatia -\frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{2}{3}+\frac{1}{16}$$

Tāpiri \frac{2}{3} ki te \frac{1}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{35}{48}$$

Tauwehea x^{2}-\frac{1}{2}x+\frac{1}{16}. 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}.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{35}{48}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{35}{48}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{\sqrt{105}}{12} x-\frac{1}{4}=-\frac{\sqrt{105}}{12}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{105}}{12}+\frac{1}{4} x=-\frac{\sqrt{105}}{12}+\frac{1}{4}$$