Whakaoti i te x^2+19x+100=9648

$${ x }^{ 2 } +19x+100=9648$$

Whakaoti mō x

$$x = \frac{\sqrt{38553} - 19}{2} \approx 88.67458938$$

$$x=\frac{-\sqrt{38553}-19}{2}\approx -107.67458938$$

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.

$$x^{2}+19x+100=9648$$

Me tango 9648 mai i ngā taha e rua o te whārite.

$$x^{2}+19x+100-9648=9648-9648$$

Mā te tango i te 9648 i a ia ake anō ka toe ko te 0.

$$x^{2}+19x+100-9648=0$$

Tango 9648 mai i 100.

$$x^{2}+19x-9548=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 19 mō b, me -9548 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-19±\sqrt{19^{2}-4\left(-9548\right)}}{2}$$

Pūrua 19.

$$x=\frac{-19±\sqrt{361-4\left(-9548\right)}}{2}$$

Whakareatia -4 ki te -9548.

$$x=\frac{-19±\sqrt{361+38192}}{2}$$

Tāpiri 361 ki te 38192.

$$x=\frac{-19±\sqrt{38553}}{2}$$

Nā, me whakaoti te whārite x=\frac{-19±\sqrt{38553}}{2} ina he tāpiri te ±. Tāpiri -19 ki te \sqrt{38553}.

$$x=\frac{\sqrt{38553}-19}{2}$$

Nā, me whakaoti te whārite x=\frac{-19±\sqrt{38553}}{2} ina he tango te ±. Tango \sqrt{38553} mai i -19.

$$x=\frac{-\sqrt{38553}-19}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{38553}-19}{2} x=\frac{-\sqrt{38553}-19}{2}$$

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.

$$x^{2}+19x+100=9648$$

Me tango 100 mai i ngā taha e rua o te whārite.

$$x^{2}+19x+100-100=9648-100$$

Mā te tango i te 100 i a ia ake anō ka toe ko te 0.

$$x^{2}+19x=9648-100$$

Tango 100 mai i 9648.

$$x^{2}+19x=9548$$

Whakawehea te 19, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{19}{2}. Nā, tāpiria te pūrua o te \frac{19}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+19x+\left(\frac{19}{2}\right)^{2}=9548+\left(\frac{19}{2}\right)^{2}$$

Pūruatia \frac{19}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+19x+\frac{361}{4}=9548+\frac{361}{4}$$

Tāpiri 9548 ki te \frac{361}{4}.

$$x^{2}+19x+\frac{361}{4}=\frac{38553}{4}$$

Tauwehea x^{2}+19x+\frac{361}{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}.

$$\left(x+\frac{19}{2}\right)^{2}=\frac{38553}{4}$$

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

$$\sqrt{\left(x+\frac{19}{2}\right)^{2}}=\sqrt{\frac{38553}{4}}$$

Whakarūnātia.

$$x+\frac{19}{2}=\frac{\sqrt{38553}}{2} x+\frac{19}{2}=-\frac{\sqrt{38553}}{2}$$

Me tango \frac{19}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{38553}-19}{2} x=\frac{-\sqrt{38553}-19}{2}$$