Whakaoti i te 0=2c^2-10c-24

$$0 = 2 c ^ { 2 } - 10 c - 24$$

Whakaoti mō c

$$c = \frac{\sqrt{73} + 5}{2} \approx 6.772001873$$

$$c=\frac{5-\sqrt{73}}{2}\approx -1.772001873$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2c^{2}-10c-24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -10 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Pūrua -10.

$$c=\frac{-\left(-10\right)±\sqrt{100-4\times 2\left(-24\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$c=\frac{-\left(-10\right)±\sqrt{100-8\left(-24\right)}}{2\times 2}$$

Whakareatia -8 ki te -24.

$$c=\frac{-\left(-10\right)±\sqrt{100+192}}{2\times 2}$$

Tāpiri 100 ki te 192.

$$c=\frac{-\left(-10\right)±\sqrt{292}}{2\times 2}$$

Tuhia te pūtakerua o te 292.

$$c=\frac{-\left(-10\right)±2\sqrt{73}}{2\times 2}$$

Ko te tauaro o -10 ko 10.

$$c=\frac{10±2\sqrt{73}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$c=\frac{10±2\sqrt{73}}{4}$$

Nā, me whakaoti te whārite c=\frac{10±2\sqrt{73}}{4} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{73}.

$$c=\frac{2\sqrt{73}+10}{4}$$

Whakawehe 10+2\sqrt{73} ki te 4.

$$c=\frac{\sqrt{73}+5}{2}$$

Nā, me whakaoti te whārite c=\frac{10±2\sqrt{73}}{4} ina he tango te ±. Tango 2\sqrt{73} mai i 10.

$$c=\frac{10-2\sqrt{73}}{4}$$

Whakawehe 10-2\sqrt{73} ki te 4.

$$c=\frac{5-\sqrt{73}}{2}$$

Kua oti te whārite te whakatau.

$$c=\frac{\sqrt{73}+5}{2} c=\frac{5-\sqrt{73}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2c^{2}-10c-24=0$$

Me tāpiri te 24 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2c^{2}-10c=24$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2c^{2}-10c}{2}=\frac{24}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$c^{2}+\left(-\frac{10}{2}\right)c=\frac{24}{2}$$

Whakawehe -10 ki te 2.

$$c^{2}-5c=\frac{24}{2}$$

Whakawehe 24 ki te 2.

$$c^{2}-5c=12$$

Whakawehea te -5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{2}. Nā, tāpiria te pūrua o te -\frac{5}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$c^{2}-5c+\left(-\frac{5}{2}\right)^{2}=12+\left(-\frac{5}{2}\right)^{2}$$

Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$c^{2}-5c+\frac{25}{4}=12+\frac{25}{4}$$

Tāpiri 12 ki te \frac{25}{4}.

$$c^{2}-5c+\frac{25}{4}=\frac{73}{4}$$

Tauwehea c^{2}-5c+\frac{25}{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}.

$$\left(c-\frac{5}{2}\right)^{2}=\frac{73}{4}$$

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

$$\sqrt{\left(c-\frac{5}{2}\right)^{2}}=\sqrt{\frac{73}{4}}$$

Whakarūnātia.

$$c-\frac{5}{2}=\frac{\sqrt{73}}{2} c-\frac{5}{2}=-\frac{\sqrt{73}}{2}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$c=\frac{\sqrt{73}+5}{2} c=\frac{5-\sqrt{73}}{2}$$