Whakaoti i te 0=a^2+5a-40

$$0 = a ^ { 2 } + 5 a - 40$$

Whakaoti mō a

$$a = \frac{\sqrt{185} - 5}{2} \approx 4.300735254$$

$$a=\frac{-\sqrt{185}-5}{2}\approx -9.300735254$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$a^{2}+5a-40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me -40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-5±\sqrt{5^{2}-4\left(-40\right)}}{2}$$

Pūrua 5.

$$a=\frac{-5±\sqrt{25-4\left(-40\right)}}{2}$$

Whakareatia -4 ki te -40.

$$a=\frac{-5±\sqrt{25+160}}{2}$$

Tāpiri 25 ki te 160.

$$a=\frac{-5±\sqrt{185}}{2}$$

Nā, me whakaoti te whārite a=\frac{-5±\sqrt{185}}{2} ina he tāpiri te ±. Tāpiri -5 ki te \sqrt{185}.

$$a=\frac{\sqrt{185}-5}{2}$$

Nā, me whakaoti te whārite a=\frac{-5±\sqrt{185}}{2} ina he tango te ±. Tango \sqrt{185} mai i -5.

$$a=\frac{-\sqrt{185}-5}{2}$$

Kua oti te whārite te whakatau.

$$a=\frac{\sqrt{185}-5}{2} a=\frac{-\sqrt{185}-5}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$a^{2}+5a-40=0$$

Me tāpiri te 40 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$a^{2}+5a=40$$

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.

$$a^{2}+5a+\left(\frac{5}{2}\right)^{2}=40+\left(\frac{5}{2}\right)^{2}$$

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

$$a^{2}+5a+\frac{25}{4}=40+\frac{25}{4}$$

Tāpiri 40 ki te \frac{25}{4}.

$$a^{2}+5a+\frac{25}{4}=\frac{185}{4}$$

Tauwehea a^{2}+5a+\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}.

$$\left(a+\frac{5}{2}\right)^{2}=\frac{185}{4}$$

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

$$\sqrt{\left(a+\frac{5}{2}\right)^{2}}=\sqrt{\frac{185}{4}}$$

Whakarūnātia.

$$a+\frac{5}{2}=\frac{\sqrt{185}}{2} a+\frac{5}{2}=-\frac{\sqrt{185}}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$a=\frac{\sqrt{185}-5}{2} a=\frac{-\sqrt{185}-5}{2}$$