Whakaoti i te z^2+16z+64=7

$$z ^ { 2 } + 16 z + 64 = 7$$

Whakaoti mō z (complex solution)

$$z=\sqrt{7}-8\approx -5.354248689$$

$$z=-\left(\sqrt{7}+8\right)\approx -10.645751311$$

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.

$$z^{2}+16z+64=7$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$z^{2}+16z+64-7=7-7$$

Mā te tango i te 7 i a ia ake anō ka toe ko te 0.

$$z^{2}+16z+64-7=0$$

Tango 7 mai i 64.

$$z^{2}+16z+57=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me 57 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{-16±\sqrt{16^{2}-4\times 57}}{2}$$

Pūrua 16.

$$z=\frac{-16±\sqrt{256-4\times 57}}{2}$$

Whakareatia -4 ki te 57.

$$z=\frac{-16±\sqrt{256-228}}{2}$$

Tāpiri 256 ki te -228.

$$z=\frac{-16±\sqrt{28}}{2}$$

Tuhia te pūtakerua o te 28.

$$z=\frac{-16±2\sqrt{7}}{2}$$

Nā, me whakaoti te whārite z=\frac{-16±2\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{7}.

$$z=\frac{2\sqrt{7}-16}{2}$$

Whakawehe -16+2\sqrt{7} ki te 2.

$$z=\sqrt{7}-8$$

Nā, me whakaoti te whārite z=\frac{-16±2\sqrt{7}}{2} ina he tango te ±. Tango 2\sqrt{7} mai i -16.

$$z=\frac{-2\sqrt{7}-16}{2}$$

Whakawehe -16-2\sqrt{7} ki te 2.

$$z=-\sqrt{7}-8$$

Kua oti te whārite te whakatau.

$$z=\sqrt{7}-8 z=-\sqrt{7}-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Tauwehea z^{2}+16z+64. 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}.

$$\left(z+8\right)^{2}=7$$

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

$$\sqrt{\left(z+8\right)^{2}}=\sqrt{7}$$

Whakarūnātia.

$$z+8=\sqrt{7} z+8=-\sqrt{7}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$z=\sqrt{7}-8 z=-\sqrt{7}-8$$

Whakaoti mō z

$$z=\sqrt{7}-8\approx -5.354248689$$

$$z=-\sqrt{7}-8\approx -10.645751311$$

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.

$$z^{2}+16z+64=7$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$z^{2}+16z+64-7=7-7$$

Mā te tango i te 7 i a ia ake anō ka toe ko te 0.

$$z^{2}+16z+64-7=0$$

Tango 7 mai i 64.

$$z^{2}+16z+57=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me 57 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{-16±\sqrt{16^{2}-4\times 57}}{2}$$

Pūrua 16.

$$z=\frac{-16±\sqrt{256-4\times 57}}{2}$$

Whakareatia -4 ki te 57.

$$z=\frac{-16±\sqrt{256-228}}{2}$$

Tāpiri 256 ki te -228.

$$z=\frac{-16±\sqrt{28}}{2}$$

Tuhia te pūtakerua o te 28.

$$z=\frac{-16±2\sqrt{7}}{2}$$

Nā, me whakaoti te whārite z=\frac{-16±2\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{7}.

$$z=\frac{2\sqrt{7}-16}{2}$$

Whakawehe -16+2\sqrt{7} ki te 2.

$$z=\sqrt{7}-8$$

Nā, me whakaoti te whārite z=\frac{-16±2\sqrt{7}}{2} ina he tango te ±. Tango 2\sqrt{7} mai i -16.

$$z=\frac{-2\sqrt{7}-16}{2}$$

Whakawehe -16-2\sqrt{7} ki te 2.

$$z=-\sqrt{7}-8$$

Kua oti te whārite te whakatau.

$$z=\sqrt{7}-8 z=-\sqrt{7}-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Tauwehea z^{2}+16z+64. 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}.

$$\left(z+8\right)^{2}=7$$

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

$$\sqrt{\left(z+8\right)^{2}}=\sqrt{7}$$

Whakarūnātia.

$$z+8=\sqrt{7} z+8=-\sqrt{7}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$z=\sqrt{7}-8 z=-\sqrt{7}-8$$