Whakaoti i te x^2+49x=360

$$x ^ { 2 } + 49 x = 360$$

Whakaoti mō x

$$x = \frac{\sqrt{3841} - 49}{2} \approx 6.487900865$$

$$x=\frac{-\sqrt{3841}-49}{2}\approx -55.487900865$$

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.

$$x^{2}+49x=360$$

Me tango 360 mai i ngā taha e rua o te whārite.

$$x^{2}+49x-360=360-360$$

Mā te tango i te 360 i a ia ake anō ka toe ko te 0.

$$x^{2}+49x-360=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 49 mō b, me -360 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-49±\sqrt{49^{2}-4\left(-360\right)}}{2}$$

Pūrua 49.

$$x=\frac{-49±\sqrt{2401-4\left(-360\right)}}{2}$$

Whakareatia -4 ki te -360.

$$x=\frac{-49±\sqrt{2401+1440}}{2}$$

Tāpiri 2401 ki te 1440.

$$x=\frac{-49±\sqrt{3841}}{2}$$

Nā, me whakaoti te whārite x=\frac{-49±\sqrt{3841}}{2} ina he tāpiri te ±. Tāpiri -49 ki te \sqrt{3841}.

$$x=\frac{\sqrt{3841}-49}{2}$$

Nā, me whakaoti te whārite x=\frac{-49±\sqrt{3841}}{2} ina he tango te ±. Tango \sqrt{3841} mai i -49.

$$x=\frac{-\sqrt{3841}-49}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{3841}-49}{2} x=\frac{-\sqrt{3841}-49}{2}$$

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.

$$x^{2}+49x=360$$

Whakawehea te 49, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{49}{2}. Nā, tāpiria te pūrua o te \frac{49}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+49x+\left(\frac{49}{2}\right)^{2}=360+\left(\frac{49}{2}\right)^{2}$$

Pūruatia \frac{49}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+49x+\frac{2401}{4}=360+\frac{2401}{4}$$

Tāpiri 360 ki te \frac{2401}{4}.

$$x^{2}+49x+\frac{2401}{4}=\frac{3841}{4}$$

Tauwehea x^{2}+49x+\frac{2401}{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}.

$$\left(x+\frac{49}{2}\right)^{2}=\frac{3841}{4}$$

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

$$\sqrt{\left(x+\frac{49}{2}\right)^{2}}=\sqrt{\frac{3841}{4}}$$

Whakarūnātia.

$$x+\frac{49}{2}=\frac{\sqrt{3841}}{2} x+\frac{49}{2}=-\frac{\sqrt{3841}}{2}$$

Me tango \frac{49}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{3841}-49}{2} x=\frac{-\sqrt{3841}-49}{2}$$