Whakaoti i te -2x^2+6x-10=-3x^2

$$- 2 x ^ { 2 } + 6 x - 10 = - 3 x ^ { 2 }$$

Whakaoti mō x (complex solution)

$$x=\sqrt{19}-3\approx 1.358898944$$

$$x=-\left(\sqrt{19}+3\right)\approx -7.358898944$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$-2x^{2}+6x-10+3x^{2}=0$$

Pahekotia te -2x^{2} me 3x^{2}, ka x^{2}.

$$x^{2}+6x-10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-10\right)}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-10\right)}}{2}$$

Whakareatia -4 ki te -10.

$$x=\frac{-6±\sqrt{36+40}}{2}$$

Tāpiri 36 ki te 40.

$$x=\frac{-6±\sqrt{76}}{2}$$

Tuhia te pūtakerua o te 76.

$$x=\frac{-6±2\sqrt{19}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{19}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{19}.

$$x=\frac{2\sqrt{19}-6}{2}$$

Whakawehe -6+2\sqrt{19} ki te 2.

$$x=\sqrt{19}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{19}}{2} ina he tango te ±. Tango 2\sqrt{19} mai i -6.

$$x=\frac{-2\sqrt{19}-6}{2}$$

Whakawehe -6-2\sqrt{19} ki te 2.

$$x=-\sqrt{19}-3$$

Kua oti te whārite te whakatau.

$$x=\sqrt{19}-3 x=-\sqrt{19}-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$-2x^{2}+6x-10+3x^{2}=0$$

Pahekotia te -2x^{2} me 3x^{2}, ka x^{2}.

$$x^{2}+6x-10=0$$

Me tāpiri te 10 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}+6x=10$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+6x+3^{2}=10+3^{2}$$

Pūrua 3.

$$x^{2}+6x+9=10+9$$

Tāpiri 10 ki te 9.

$$x^{2}+6x+9=19$$

Tauwehea x^{2}+6x+9. 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}.

$$\left(x+3\right)^{2}=19$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{19}$$

Whakarūnātia.

$$x+3=\sqrt{19} x+3=-\sqrt{19}$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$x=\sqrt{19}-3 x=-\sqrt{19}-3$$

Whakaoti mō x

$$x=\sqrt{19}-3\approx 1.358898944$$

$$x=-\sqrt{19}-3\approx -7.358898944$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$-2x^{2}+6x-10+3x^{2}=0$$

Pahekotia te -2x^{2} me 3x^{2}, ka x^{2}.

$$x^{2}+6x-10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-10\right)}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-10\right)}}{2}$$

Whakareatia -4 ki te -10.

$$x=\frac{-6±\sqrt{36+40}}{2}$$

Tāpiri 36 ki te 40.

$$x=\frac{-6±\sqrt{76}}{2}$$

Tuhia te pūtakerua o te 76.

$$x=\frac{-6±2\sqrt{19}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{19}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{19}.

$$x=\frac{2\sqrt{19}-6}{2}$$

Whakawehe -6+2\sqrt{19} ki te 2.

$$x=\sqrt{19}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{19}}{2} ina he tango te ±. Tango 2\sqrt{19} mai i -6.

$$x=\frac{-2\sqrt{19}-6}{2}$$

Whakawehe -6-2\sqrt{19} ki te 2.

$$x=-\sqrt{19}-3$$

Kua oti te whārite te whakatau.

$$x=\sqrt{19}-3 x=-\sqrt{19}-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$-2x^{2}+6x-10+3x^{2}=0$$

Pahekotia te -2x^{2} me 3x^{2}, ka x^{2}.

$$x^{2}+6x-10=0$$

Me tāpiri te 10 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}+6x=10$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+6x+3^{2}=10+3^{2}$$

Pūrua 3.

$$x^{2}+6x+9=10+9$$

Tāpiri 10 ki te 9.

$$x^{2}+6x+9=19$$

Tauwehea x^{2}+6x+9. 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}.

$$\left(x+3\right)^{2}=19$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{19}$$

Whakarūnātia.

$$x+3=\sqrt{19} x+3=-\sqrt{19}$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$x=\sqrt{19}-3 x=-\sqrt{19}-3$$