Whakaoti i te (x+2)(x+4)=12

$$( x + 2 ) ( x + 4 ) = 12$$

Whakaoti mō x (complex solution)

$$x=\sqrt{13}-3\approx 0.605551275$$

$$x=-\left(\sqrt{13}+3\right)\approx -6.605551275$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+4 ka whakakotahi i ngā kupu rite.

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

Tangohia te 12 mai i ngā taha e rua.

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

Tangohia te 12 i te 8, ka -4.

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

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

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

Pūrua 6.

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

Whakareatia -4 ki te -4.

$$x=\frac{-6±\sqrt{36+16}}{2}$$

Tāpiri 36 ki te 16.

$$x=\frac{-6±\sqrt{52}}{2}$$

Tuhia te pūtakerua o te 52.

$$x=\frac{-6±2\sqrt{13}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{13}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{13}.

$$x=\frac{2\sqrt{13}-6}{2}$$

Whakawehe -6+2\sqrt{13} ki te 2.

$$x=\sqrt{13}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{13}}{2} ina he tango te ±. Tango 2\sqrt{13} mai i -6.

$$x=\frac{-2\sqrt{13}-6}{2}$$

Whakawehe -6-2\sqrt{13} ki te 2.

$$x=-\sqrt{13}-3$$

Kua oti te whārite te whakatau.

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+4 ka whakakotahi i ngā kupu rite.

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

Tangohia te 8 mai i ngā taha e rua.

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

Tangohia te 8 i te 12, ka 4.

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

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.

$$x^{2}+6x+3^{2}=4+3^{2}$$

Pūrua 3.

$$x^{2}+6x+9=4+9$$

Tāpiri 4 ki te 9.

$$x^{2}+6x+9=13$$

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}.

$$\left(x+3\right)^{2}=13$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{13}$$

Whakarūnātia.

$$x+3=\sqrt{13} x+3=-\sqrt{13}$$

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

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$

Whakaoti mō x

$$x=\sqrt{13}-3\approx 0.605551275$$

$$x=-\sqrt{13}-3\approx -6.605551275$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+4 ka whakakotahi i ngā kupu rite.

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

Tangohia te 12 mai i ngā taha e rua.

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

Tangohia te 12 i te 8, ka -4.

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

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

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

Pūrua 6.

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

Whakareatia -4 ki te -4.

$$x=\frac{-6±\sqrt{36+16}}{2}$$

Tāpiri 36 ki te 16.

$$x=\frac{-6±\sqrt{52}}{2}$$

Tuhia te pūtakerua o te 52.

$$x=\frac{-6±2\sqrt{13}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{13}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{13}.

$$x=\frac{2\sqrt{13}-6}{2}$$

Whakawehe -6+2\sqrt{13} ki te 2.

$$x=\sqrt{13}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{13}}{2} ina he tango te ±. Tango 2\sqrt{13} mai i -6.

$$x=\frac{-2\sqrt{13}-6}{2}$$

Whakawehe -6-2\sqrt{13} ki te 2.

$$x=-\sqrt{13}-3$$

Kua oti te whārite te whakatau.

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+4 ka whakakotahi i ngā kupu rite.

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

Tangohia te 8 mai i ngā taha e rua.

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

Tangohia te 8 i te 12, ka 4.

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

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.

$$x^{2}+6x+3^{2}=4+3^{2}$$

Pūrua 3.

$$x^{2}+6x+9=4+9$$

Tāpiri 4 ki te 9.

$$x^{2}+6x+9=13$$

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}.

$$\left(x+3\right)^{2}=13$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{13}$$

Whakarūnātia.

$$x+3=\sqrt{13} x+3=-\sqrt{13}$$

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

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$