Whakaoti i te x^2+85x=550

$$x ^ { 2 } + 85 x = 550$$

Whakaoti mō x

$$x = \frac{5 \sqrt{377} - 85}{2} \approx 6.041219597$$

$$x=\frac{-5\sqrt{377}-85}{2}\approx -91.041219597$$

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.

$$x^{2}+85x=550$$

Me tango 550 mai i ngā taha e rua o te whārite.

$$x^{2}+85x-550=550-550$$

Mā te tango i te 550 i a ia ake anō ka toe ko te 0.

$$x^{2}+85x-550=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 85 mō b, me -550 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-85±\sqrt{85^{2}-4\left(-550\right)}}{2}$$

Pūrua 85.

$$x=\frac{-85±\sqrt{7225-4\left(-550\right)}}{2}$$

Whakareatia -4 ki te -550.

$$x=\frac{-85±\sqrt{7225+2200}}{2}$$

Tāpiri 7225 ki te 2200.

$$x=\frac{-85±\sqrt{9425}}{2}$$

Tuhia te pūtakerua o te 9425.

$$x=\frac{-85±5\sqrt{377}}{2}$$

Nā, me whakaoti te whārite x=\frac{-85±5\sqrt{377}}{2} ina he tāpiri te ±. Tāpiri -85 ki te 5\sqrt{377}.

$$x=\frac{5\sqrt{377}-85}{2}$$

Nā, me whakaoti te whārite x=\frac{-85±5\sqrt{377}}{2} ina he tango te ±. Tango 5\sqrt{377} mai i -85.

$$x=\frac{-5\sqrt{377}-85}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{5\sqrt{377}-85}{2} x=\frac{-5\sqrt{377}-85}{2}$$

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.

$$x^{2}+85x=550$$

Whakawehea te 85, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{85}{2}. Nā, tāpiria te pūrua o te \frac{85}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+85x+\left(\frac{85}{2}\right)^{2}=550+\left(\frac{85}{2}\right)^{2}$$

Pūruatia \frac{85}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+85x+\frac{7225}{4}=550+\frac{7225}{4}$$

Tāpiri 550 ki te \frac{7225}{4}.

$$x^{2}+85x+\frac{7225}{4}=\frac{9425}{4}$$

Tauwehea x^{2}+85x+\frac{7225}{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}.

$$\left(x+\frac{85}{2}\right)^{2}=\frac{9425}{4}$$

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

$$\sqrt{\left(x+\frac{85}{2}\right)^{2}}=\sqrt{\frac{9425}{4}}$$

Whakarūnātia.

$$x+\frac{85}{2}=\frac{5\sqrt{377}}{2} x+\frac{85}{2}=-\frac{5\sqrt{377}}{2}$$

Me tango \frac{85}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{5\sqrt{377}-85}{2} x=\frac{-5\sqrt{377}-85}{2}$$