Whakaoti i te w^2+14w-136=0

$$w ^ { 2 } + 14 w - 136 = 0$$

Whakaoti mō w (complex solution)

$$w=\sqrt{185}-7\approx 6.601470509$$

$$w=-\left(\sqrt{185}+7\right)\approx -20.601470509$$

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.

$$w^{2}+14w-136=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 14 mō b, me -136 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-14±\sqrt{14^{2}-4\left(-136\right)}}{2}$$

Pūrua 14.

$$w=\frac{-14±\sqrt{196-4\left(-136\right)}}{2}$$

Whakareatia -4 ki te -136.

$$w=\frac{-14±\sqrt{196+544}}{2}$$

Tāpiri 196 ki te 544.

$$w=\frac{-14±\sqrt{740}}{2}$$

Tuhia te pūtakerua o te 740.

$$w=\frac{-14±2\sqrt{185}}{2}$$

Nā, me whakaoti te whārite w=\frac{-14±2\sqrt{185}}{2} ina he tāpiri te ±. Tāpiri -14 ki te 2\sqrt{185}.

$$w=\frac{2\sqrt{185}-14}{2}$$

Whakawehe -14+2\sqrt{185} ki te 2.

$$w=\sqrt{185}-7$$

Nā, me whakaoti te whārite w=\frac{-14±2\sqrt{185}}{2} ina he tango te ±. Tango 2\sqrt{185} mai i -14.

$$w=\frac{-2\sqrt{185}-14}{2}$$

Whakawehe -14-2\sqrt{185} ki te 2.

$$w=-\sqrt{185}-7$$

Kua oti te whārite te whakatau.

$$w=\sqrt{185}-7 w=-\sqrt{185}-7$$

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.

$$w^{2}+14w-136=0$$

Me tāpiri 136 ki ngā taha e rua o te whārite.

$$w^{2}+14w-136-\left(-136\right)=-\left(-136\right)$$

Mā te tango i te -136 i a ia ake anō ka toe ko te 0.

$$w^{2}+14w=-\left(-136\right)$$

Tango -136 mai i 0.

$$w^{2}+14w=136$$

Whakawehea te 14, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 7. Nā, tāpiria te pūrua o te 7 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$w^{2}+14w+7^{2}=136+7^{2}$$

Pūrua 7.

$$w^{2}+14w+49=136+49$$

Tāpiri 136 ki te 49.

$$w^{2}+14w+49=185$$

Tauwehea w^{2}+14w+49. 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}.

$$\left(w+7\right)^{2}=185$$

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

$$\sqrt{\left(w+7\right)^{2}}=\sqrt{185}$$

Whakarūnātia.

$$w+7=\sqrt{185} w+7=-\sqrt{185}$$

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

$$w=\sqrt{185}-7 w=-\sqrt{185}-7$$

Whakaoti mō w

$$w=\sqrt{185}-7\approx 6.601470509$$

$$w=-\sqrt{185}-7\approx -20.601470509$$

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.

$$w^{2}+14w-136=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 14 mō b, me -136 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-14±\sqrt{14^{2}-4\left(-136\right)}}{2}$$

Pūrua 14.

$$w=\frac{-14±\sqrt{196-4\left(-136\right)}}{2}$$

Whakareatia -4 ki te -136.

$$w=\frac{-14±\sqrt{196+544}}{2}$$

Tāpiri 196 ki te 544.

$$w=\frac{-14±\sqrt{740}}{2}$$

Tuhia te pūtakerua o te 740.

$$w=\frac{-14±2\sqrt{185}}{2}$$

Nā, me whakaoti te whārite w=\frac{-14±2\sqrt{185}}{2} ina he tāpiri te ±. Tāpiri -14 ki te 2\sqrt{185}.

$$w=\frac{2\sqrt{185}-14}{2}$$

Whakawehe -14+2\sqrt{185} ki te 2.

$$w=\sqrt{185}-7$$

Nā, me whakaoti te whārite w=\frac{-14±2\sqrt{185}}{2} ina he tango te ±. Tango 2\sqrt{185} mai i -14.

$$w=\frac{-2\sqrt{185}-14}{2}$$

Whakawehe -14-2\sqrt{185} ki te 2.

$$w=-\sqrt{185}-7$$

Kua oti te whārite te whakatau.

$$w=\sqrt{185}-7 w=-\sqrt{185}-7$$

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.

$$w^{2}+14w-136=0$$

Me tāpiri 136 ki ngā taha e rua o te whārite.

$$w^{2}+14w-136-\left(-136\right)=-\left(-136\right)$$

Mā te tango i te -136 i a ia ake anō ka toe ko te 0.

$$w^{2}+14w=-\left(-136\right)$$

Tango -136 mai i 0.

$$w^{2}+14w=136$$

Whakawehea te 14, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 7. Nā, tāpiria te pūrua o te 7 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$w^{2}+14w+7^{2}=136+7^{2}$$

Pūrua 7.

$$w^{2}+14w+49=136+49$$

Tāpiri 136 ki te 49.

$$w^{2}+14w+49=185$$

Tauwehea w^{2}+14w+49. 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}.

$$\left(w+7\right)^{2}=185$$

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

$$\sqrt{\left(w+7\right)^{2}}=\sqrt{185}$$

Whakarūnātia.

$$w+7=\sqrt{185} w+7=-\sqrt{185}$$

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

$$w=\sqrt{185}-7 w=-\sqrt{185}-7$$