Whakaoti i te c^2+4c-17=-6

$$c ^ { 2 } + 4 c - 17 = - 6$$

Whakaoti mō c

$$c=\sqrt{15}-2\approx 1.872983346$$

$$c=-\sqrt{15}-2\approx -5.872983346$$

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.

$$c^{2}+4c-17=-6$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$c^{2}+4c-17-\left(-6\right)=-6-\left(-6\right)$$

Mā te tango i te -6 i a ia ake anō ka toe ko te 0.

$$c^{2}+4c-17-\left(-6\right)=0$$

Tango -6 mai i -17.

$$c^{2}+4c-11=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -11 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{-4±\sqrt{4^{2}-4\left(-11\right)}}{2}$$

Pūrua 4.

$$c=\frac{-4±\sqrt{16-4\left(-11\right)}}{2}$$

Whakareatia -4 ki te -11.

$$c=\frac{-4±\sqrt{16+44}}{2}$$

Tāpiri 16 ki te 44.

$$c=\frac{-4±\sqrt{60}}{2}$$

Tuhia te pūtakerua o te 60.

$$c=\frac{-4±2\sqrt{15}}{2}$$

Nā, me whakaoti te whārite c=\frac{-4±2\sqrt{15}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{15}.

$$c=\frac{2\sqrt{15}-4}{2}$$

Whakawehe -4+2\sqrt{15} ki te 2.

$$c=\sqrt{15}-2$$

Nā, me whakaoti te whārite c=\frac{-4±2\sqrt{15}}{2} ina he tango te ±. Tango 2\sqrt{15} mai i -4.

$$c=\frac{-2\sqrt{15}-4}{2}$$

Whakawehe -4-2\sqrt{15} ki te 2.

$$c=-\sqrt{15}-2$$

Kua oti te whārite te whakatau.

$$c=\sqrt{15}-2 c=-\sqrt{15}-2$$

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.

$$c^{2}+4c-17=-6$$

Me tāpiri 17 ki ngā taha e rua o te whārite.

$$c^{2}+4c-17-\left(-17\right)=-6-\left(-17\right)$$

Mā te tango i te -17 i a ia ake anō ka toe ko te 0.

$$c^{2}+4c=-6-\left(-17\right)$$

Tango -17 mai i -6.

$$c^{2}+4c=11$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$c^{2}+4c+2^{2}=11+2^{2}$$

Pūrua 2.

$$c^{2}+4c+4=11+4$$

Tāpiri 11 ki te 4.

$$c^{2}+4c+4=15$$

Tauwehea c^{2}+4c+4. 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}.

$$\left(c+2\right)^{2}=15$$

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

$$\sqrt{\left(c+2\right)^{2}}=\sqrt{15}$$

Whakarūnātia.

$$c+2=\sqrt{15} c+2=-\sqrt{15}$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$c=\sqrt{15}-2 c=-\sqrt{15}-2$$