Whakaoti i te y^2+10=-12y

$$y ^ { 2 } + 10 = - 12 y$$

Whakaoti mō y (complex solution)

$$y=\sqrt{26}-6\approx -0.900980486$$

$$y=-\left(\sqrt{26}+6\right)\approx -11.099019514$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 12y ki ngā taha e rua.

$$y^{2}+10+12y=0$$

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.

$$y^{2}+12y+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-12±\sqrt{12^{2}-4\times 10}}{2}$$

Pūrua 12.

$$y=\frac{-12±\sqrt{144-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$y=\frac{-12±\sqrt{144-40}}{2}$$

Tāpiri 144 ki te -40.

$$y=\frac{-12±\sqrt{104}}{2}$$

Tuhia te pūtakerua o te 104.

$$y=\frac{-12±2\sqrt{26}}{2}$$

Nā, me whakaoti te whārite y=\frac{-12±2\sqrt{26}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{26}.

$$y=\frac{2\sqrt{26}-12}{2}$$

Whakawehe -12+2\sqrt{26} ki te 2.

$$y=\sqrt{26}-6$$

Nā, me whakaoti te whārite y=\frac{-12±2\sqrt{26}}{2} ina he tango te ±. Tango 2\sqrt{26} mai i -12.

$$y=\frac{-2\sqrt{26}-12}{2}$$

Whakawehe -12-2\sqrt{26} ki te 2.

$$y=-\sqrt{26}-6$$

Kua oti te whārite te whakatau.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 12y ki ngā taha e rua.

$$y^{2}+10+12y=0$$

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y^{2}+12y=-10$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}+12y+6^{2}=-10+6^{2}$$

Pūrua 6.

$$y^{2}+12y+36=-10+36$$

Tāpiri -10 ki te 36.

$$y^{2}+12y+36=26$$

Tauwehea y^{2}+12y+36. 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}.

$$\left(y+6\right)^{2}=26$$

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

$$\sqrt{\left(y+6\right)^{2}}=\sqrt{26}$$

Whakarūnātia.

$$y+6=\sqrt{26} y+6=-\sqrt{26}$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$

Whakaoti mō y

$$y=\sqrt{26}-6\approx -0.900980486$$

$$y=-\sqrt{26}-6\approx -11.099019514$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 12y ki ngā taha e rua.

$$y^{2}+10+12y=0$$

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.

$$y^{2}+12y+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-12±\sqrt{12^{2}-4\times 10}}{2}$$

Pūrua 12.

$$y=\frac{-12±\sqrt{144-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$y=\frac{-12±\sqrt{144-40}}{2}$$

Tāpiri 144 ki te -40.

$$y=\frac{-12±\sqrt{104}}{2}$$

Tuhia te pūtakerua o te 104.

$$y=\frac{-12±2\sqrt{26}}{2}$$

Nā, me whakaoti te whārite y=\frac{-12±2\sqrt{26}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{26}.

$$y=\frac{2\sqrt{26}-12}{2}$$

Whakawehe -12+2\sqrt{26} ki te 2.

$$y=\sqrt{26}-6$$

Nā, me whakaoti te whārite y=\frac{-12±2\sqrt{26}}{2} ina he tango te ±. Tango 2\sqrt{26} mai i -12.

$$y=\frac{-2\sqrt{26}-12}{2}$$

Whakawehe -12-2\sqrt{26} ki te 2.

$$y=-\sqrt{26}-6$$

Kua oti te whārite te whakatau.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 12y ki ngā taha e rua.

$$y^{2}+10+12y=0$$

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y^{2}+12y=-10$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}+12y+6^{2}=-10+6^{2}$$

Pūrua 6.

$$y^{2}+12y+36=-10+36$$

Tāpiri -10 ki te 36.

$$y^{2}+12y+36=26$$

Tauwehea y^{2}+12y+36. 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}.

$$\left(y+6\right)^{2}=26$$

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

$$\sqrt{\left(y+6\right)^{2}}=\sqrt{26}$$

Whakarūnātia.

$$y+6=\sqrt{26} y+6=-\sqrt{26}$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$