Whakaoti i te 6x^2+12x-1134=0

$$6 { x }^{ 2 } +12x-1134=0$$

Whakaoti mō x (complex solution)

$$x=\sqrt{190}-1\approx 12.784048752$$

$$x=-\left(\sqrt{190}+1\right)\approx -14.784048752$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$6x^{2}+12x-1134=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 12 mō b, me -1134 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 6\left(-1134\right)}}{2\times 6}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 6\left(-1134\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-12±\sqrt{144-24\left(-1134\right)}}{2\times 6}$$

Whakareatia -24 ki te -1134.

$$x=\frac{-12±\sqrt{144+27216}}{2\times 6}$$

Tāpiri 144 ki te 27216.

$$x=\frac{-12±\sqrt{27360}}{2\times 6}$$

Tuhia te pūtakerua o te 27360.

$$x=\frac{-12±12\sqrt{190}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-12±12\sqrt{190}}{12}$$

Nā, me whakaoti te whārite x=\frac{-12±12\sqrt{190}}{12} ina he tāpiri te ±. Tāpiri -12 ki te 12\sqrt{190}.

$$x=\frac{12\sqrt{190}-12}{12}$$

Whakawehe -12+12\sqrt{190} ki te 12.

$$x=\sqrt{190}-1$$

Nā, me whakaoti te whārite x=\frac{-12±12\sqrt{190}}{12} ina he tango te ±. Tango 12\sqrt{190} mai i -12.

$$x=\frac{-12\sqrt{190}-12}{12}$$

Whakawehe -12-12\sqrt{190} ki te 12.

$$x=-\sqrt{190}-1$$

Kua oti te whārite te whakatau.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$6x^{2}+12x-1134=0$$

Me tāpiri 1134 ki ngā taha e rua o te whārite.

$$6x^{2}+12x-1134-\left(-1134\right)=-\left(-1134\right)$$

Mā te tango i te -1134 i a ia ake anō ka toe ko te 0.

$$6x^{2}+12x=-\left(-1134\right)$$

Tango -1134 mai i 0.

$$6x^{2}+12x=1134$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+12x}{6}=\frac{1134}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\frac{12}{6}x=\frac{1134}{6}$$

Whakawehe 12 ki te 6.

$$x^{2}+2x=\frac{1134}{6}$$

Whakawehe 1134 ki te 6.

$$x^{2}+2x=189$$

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

$$x^{2}+2x+1^{2}=189+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=189+1$$

Tāpiri 189 ki te 1.

$$x^{2}+2x+1=190$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=190$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{190}$$

Whakarūnātia.

$$x+1=\sqrt{190} x+1=-\sqrt{190}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$

Whakaoti mō x

$$x=\sqrt{190}-1\approx 12.784048752$$

$$x=-\sqrt{190}-1\approx -14.784048752$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$6x^{2}+12x-1134=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 12 mō b, me -1134 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 6\left(-1134\right)}}{2\times 6}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 6\left(-1134\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-12±\sqrt{144-24\left(-1134\right)}}{2\times 6}$$

Whakareatia -24 ki te -1134.

$$x=\frac{-12±\sqrt{144+27216}}{2\times 6}$$

Tāpiri 144 ki te 27216.

$$x=\frac{-12±\sqrt{27360}}{2\times 6}$$

Tuhia te pūtakerua o te 27360.

$$x=\frac{-12±12\sqrt{190}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-12±12\sqrt{190}}{12}$$

Nā, me whakaoti te whārite x=\frac{-12±12\sqrt{190}}{12} ina he tāpiri te ±. Tāpiri -12 ki te 12\sqrt{190}.

$$x=\frac{12\sqrt{190}-12}{12}$$

Whakawehe -12+12\sqrt{190} ki te 12.

$$x=\sqrt{190}-1$$

Nā, me whakaoti te whārite x=\frac{-12±12\sqrt{190}}{12} ina he tango te ±. Tango 12\sqrt{190} mai i -12.

$$x=\frac{-12\sqrt{190}-12}{12}$$

Whakawehe -12-12\sqrt{190} ki te 12.

$$x=-\sqrt{190}-1$$

Kua oti te whārite te whakatau.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$6x^{2}+12x-1134=0$$

Me tāpiri 1134 ki ngā taha e rua o te whārite.

$$6x^{2}+12x-1134-\left(-1134\right)=-\left(-1134\right)$$

Mā te tango i te -1134 i a ia ake anō ka toe ko te 0.

$$6x^{2}+12x=-\left(-1134\right)$$

Tango -1134 mai i 0.

$$6x^{2}+12x=1134$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+12x}{6}=\frac{1134}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\frac{12}{6}x=\frac{1134}{6}$$

Whakawehe 12 ki te 6.

$$x^{2}+2x=\frac{1134}{6}$$

Whakawehe 1134 ki te 6.

$$x^{2}+2x=189$$

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

$$x^{2}+2x+1^{2}=189+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=189+1$$

Tāpiri 189 ki te 1.

$$x^{2}+2x+1=190$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=190$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{190}$$

Whakarūnātia.

$$x+1=\sqrt{190} x+1=-\sqrt{190}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$