Whakaoti i te x^2-135x+600=0

$$x ^ { 2 } - 135 x + 600 = 0$$

Whakaoti mō x

$$x = \frac{5 \sqrt{633} + 135}{2} \approx 130.398728127$$

$$x = \frac{135 - 5 \sqrt{633}}{2} \approx 4.601271873$$

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.

$$x^{2}-135x+600=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -135 mō b, me 600 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-135\right)±\sqrt{\left(-135\right)^{2}-4\times 600}}{2}$$

Pūrua -135.

$$x=\frac{-\left(-135\right)±\sqrt{18225-4\times 600}}{2}$$

Whakareatia -4 ki te 600.

$$x=\frac{-\left(-135\right)±\sqrt{18225-2400}}{2}$$

Tāpiri 18225 ki te -2400.

$$x=\frac{-\left(-135\right)±\sqrt{15825}}{2}$$

Tuhia te pūtakerua o te 15825.

$$x=\frac{-\left(-135\right)±5\sqrt{633}}{2}$$

Ko te tauaro o -135 ko 135.

$$x=\frac{135±5\sqrt{633}}{2}$$

Nā, me whakaoti te whārite x=\frac{135±5\sqrt{633}}{2} ina he tāpiri te ±. Tāpiri 135 ki te 5\sqrt{633}.

$$x=\frac{5\sqrt{633}+135}{2}$$

Nā, me whakaoti te whārite x=\frac{135±5\sqrt{633}}{2} ina he tango te ±. Tango 5\sqrt{633} mai i 135.

$$x=\frac{135-5\sqrt{633}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{5\sqrt{633}+135}{2} x=\frac{135-5\sqrt{633}}{2}$$

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.

$$x^{2}-135x+600=0$$

Me tango 600 mai i ngā taha e rua o te whārite.

$$x^{2}-135x+600-600=-600$$

Mā te tango i te 600 i a ia ake anō ka toe ko te 0.

$$x^{2}-135x=-600$$

Whakawehea te -135, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{135}{2}. Nā, tāpiria te pūrua o te -\frac{135}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-135x+\left(-\frac{135}{2}\right)^{2}=-600+\left(-\frac{135}{2}\right)^{2}$$

Pūruatia -\frac{135}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-135x+\frac{18225}{4}=-600+\frac{18225}{4}$$

Tāpiri -600 ki te \frac{18225}{4}.

$$x^{2}-135x+\frac{18225}{4}=\frac{15825}{4}$$

Tauwehea x^{2}-135x+\frac{18225}{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}.

$$\left(x-\frac{135}{2}\right)^{2}=\frac{15825}{4}$$

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

$$\sqrt{\left(x-\frac{135}{2}\right)^{2}}=\sqrt{\frac{15825}{4}}$$

Whakarūnātia.

$$x-\frac{135}{2}=\frac{5\sqrt{633}}{2} x-\frac{135}{2}=-\frac{5\sqrt{633}}{2}$$

Me tāpiri \frac{135}{2} ki ngā taha e rua o te whārite.

$$x=\frac{5\sqrt{633}+135}{2} x=\frac{135-5\sqrt{633}}{2}$$