Whakaoti i te a^2-60a+400=0

$$a ^ { 2 } - 60 a + 400 = 0$$

Whakaoti mō a

$$a=10\sqrt{5}+30\approx 52.360679775$$

$$a=30-10\sqrt{5}\approx 7.639320225$$

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.

$$a^{2}-60a+400=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -60 mō b, me 400 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-60\right)±\sqrt{\left(-60\right)^{2}-4\times 400}}{2}$$

Pūrua -60.

$$a=\frac{-\left(-60\right)±\sqrt{3600-4\times 400}}{2}$$

Whakareatia -4 ki te 400.

$$a=\frac{-\left(-60\right)±\sqrt{3600-1600}}{2}$$

Tāpiri 3600 ki te -1600.

$$a=\frac{-\left(-60\right)±\sqrt{2000}}{2}$$

Tuhia te pūtakerua o te 2000.

$$a=\frac{-\left(-60\right)±20\sqrt{5}}{2}$$

Ko te tauaro o -60 ko 60.

$$a=\frac{60±20\sqrt{5}}{2}$$

Nā, me whakaoti te whārite a=\frac{60±20\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 60 ki te 20\sqrt{5}.

$$a=\frac{20\sqrt{5}+60}{2}$$

Whakawehe 60+20\sqrt{5} ki te 2.

$$a=10\sqrt{5}+30$$

Nā, me whakaoti te whārite a=\frac{60±20\sqrt{5}}{2} ina he tango te ±. Tango 20\sqrt{5} mai i 60.

$$a=\frac{60-20\sqrt{5}}{2}$$

Whakawehe 60-20\sqrt{5} ki te 2.

$$a=30-10\sqrt{5}$$

Kua oti te whārite te whakatau.

$$a=10\sqrt{5}+30 a=30-10\sqrt{5}$$

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.

$$a^{2}-60a+400=0$$

Me tango 400 mai i ngā taha e rua o te whārite.

$$a^{2}-60a+400-400=-400$$

Mā te tango i te 400 i a ia ake anō ka toe ko te 0.

$$a^{2}-60a=-400$$

Whakawehea te -60, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -30. Nā, tāpiria te pūrua o te -30 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}-60a+\left(-30\right)^{2}=-400+\left(-30\right)^{2}$$

Pūrua -30.

$$a^{2}-60a+900=-400+900$$

Tāpiri -400 ki te 900.

$$a^{2}-60a+900=500$$

Tauwehea a^{2}-60a+900. 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}.

$$\left(a-30\right)^{2}=500$$

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

$$\sqrt{\left(a-30\right)^{2}}=\sqrt{500}$$

Whakarūnātia.

$$a-30=10\sqrt{5} a-30=-10\sqrt{5}$$

Me tāpiri 30 ki ngā taha e rua o te whārite.

$$a=10\sqrt{5}+30 a=30-10\sqrt{5}$$