Whakaoti i te a^2+4a=0.001

$$a ^ { 2 } + 4 a = 0.001$$

Whakaoti mō a

$$a=\frac{\sqrt{40010}}{100}-2\approx 0.000249984$$

$$a=-\frac{\sqrt{40010}}{100}-2\approx -4.000249984$$

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.

$$a^{2}+4a=0.001$$

Me tango 0.001 mai i ngā taha e rua o te whārite.

$$a^{2}+4a-0.001=0.001-0.001$$

Mā te tango i te 0.001 i a ia ake anō ka toe ko te 0.

$$a^{2}+4a-0.001=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -0.001 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-4±\sqrt{4^{2}-4\left(-0.001\right)}}{2}$$

Pūrua 4.

$$a=\frac{-4±\sqrt{16-4\left(-0.001\right)}}{2}$$

Whakareatia -4 ki te -0.001.

$$a=\frac{-4±\sqrt{16+0.004}}{2}$$

Tāpiri 16 ki te 0.004.

$$a=\frac{-4±\sqrt{16.004}}{2}$$

Tuhia te pūtakerua o te 16.004.

$$a=\frac{-4±\frac{\sqrt{40010}}{50}}{2}$$

Nā, me whakaoti te whārite a=\frac{-4±\frac{\sqrt{40010}}{50}}{2} ina he tāpiri te ±. Tāpiri -4 ki te \frac{\sqrt{40010}}{50}.

$$a=\frac{\frac{\sqrt{40010}}{50}-4}{2}$$

Whakawehe -4+\frac{\sqrt{40010}}{50} ki te 2.

$$a=\frac{\sqrt{40010}}{100}-2$$

Nā, me whakaoti te whārite a=\frac{-4±\frac{\sqrt{40010}}{50}}{2} ina he tango te ±. Tango \frac{\sqrt{40010}}{50} mai i -4.

$$a=\frac{-\frac{\sqrt{40010}}{50}-4}{2}$$

Whakawehe -4-\frac{\sqrt{40010}}{50} ki te 2.

$$a=-\frac{\sqrt{40010}}{100}-2$$

Kua oti te whārite te whakatau.

$$a=\frac{\sqrt{40010}}{100}-2 a=-\frac{\sqrt{40010}}{100}-2$$

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.

$$a^{2}+4a=0.001$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+4a+2^{2}=0.001+2^{2}$$

Pūrua 2.

$$a^{2}+4a+4=0.001+4$$

Tāpiri 0.001 ki te 4.

$$a^{2}+4a+4=4.001$$

Tauwehea a^{2}+4a+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}.

$$\left(a+2\right)^{2}=4.001$$

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

$$\sqrt{\left(a+2\right)^{2}}=\sqrt{4.001}$$

Whakarūnātia.

$$a+2=\frac{\sqrt{40010}}{100} a+2=-\frac{\sqrt{40010}}{100}$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$a=\frac{\sqrt{40010}}{100}-2 a=-\frac{\sqrt{40010}}{100}-2$$