Whakaoti i te 0.0001x^2+x-192=0

$$0.0001 x ^ { 2 } + x - 192 = 0$$

Whakaoti mō x

$$x=200\sqrt{673}-5000\approx 188.448708429$$

$$x=-200\sqrt{673}-5000\approx -10188.448708429$$

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.

$$0.0001x^{2}+x-192=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.0001 mō a, 1 mō b, me -192 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 0.0001\left(-192\right)}}{2\times 0.0001}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 0.0001\left(-192\right)}}{2\times 0.0001}$$

Whakareatia -4 ki te 0.0001.

$$x=\frac{-1±\sqrt{1-0.0004\left(-192\right)}}{2\times 0.0001}$$

Whakareatia -0.0004 ki te -192.

$$x=\frac{-1±\sqrt{1+0.0768}}{2\times 0.0001}$$

Tāpiri 1 ki te 0.0768.

$$x=\frac{-1±\sqrt{1.0768}}{2\times 0.0001}$$

Tuhia te pūtakerua o te 1.0768.

$$x=\frac{-1±\frac{\sqrt{673}}{25}}{2\times 0.0001}$$

Whakareatia 2 ki te 0.0001.

$$x=\frac{-1±\frac{\sqrt{673}}{25}}{0.0002}$$

Nā, me whakaoti te whārite x=\frac{-1±\frac{\sqrt{673}}{25}}{0.0002} ina he tāpiri te ±. Tāpiri -1 ki te \frac{\sqrt{673}}{25}.

$$x=\frac{\frac{\sqrt{673}}{25}-1}{0.0002}$$

Whakawehe -1+\frac{\sqrt{673}}{25} ki te 0.0002 mā te whakarea -1+\frac{\sqrt{673}}{25} ki te tau huripoki o 0.0002.

$$x=200\sqrt{673}-5000$$

Nā, me whakaoti te whārite x=\frac{-1±\frac{\sqrt{673}}{25}}{0.0002} ina he tango te ±. Tango \frac{\sqrt{673}}{25} mai i -1.

$$x=\frac{-\frac{\sqrt{673}}{25}-1}{0.0002}$$

Whakawehe -1-\frac{\sqrt{673}}{25} ki te 0.0002 mā te whakarea -1-\frac{\sqrt{673}}{25} ki te tau huripoki o 0.0002.

$$x=-200\sqrt{673}-5000$$

Kua oti te whārite te whakatau.

$$x=200\sqrt{673}-5000 x=-200\sqrt{673}-5000$$

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.

$$0.0001x^{2}+x-192=0$$

Me tāpiri 192 ki ngā taha e rua o te whārite.

$$0.0001x^{2}+x-192-\left(-192\right)=-\left(-192\right)$$

Mā te tango i te -192 i a ia ake anō ka toe ko te 0.

$$0.0001x^{2}+x=-\left(-192\right)$$

Tango -192 mai i 0.

$$0.0001x^{2}+x=192$$

Me whakarea ngā taha e rua ki te 10000.

$$\frac{0.0001x^{2}+x}{0.0001}=\frac{192}{0.0001}$$

Mā te whakawehe ki te 0.0001 ka wetekia te whakareanga ki te 0.0001.

$$x^{2}+\frac{1}{0.0001}x=\frac{192}{0.0001}$$

Whakawehe 1 ki te 0.0001 mā te whakarea 1 ki te tau huripoki o 0.0001.

$$x^{2}+10000x=\frac{192}{0.0001}$$

Whakawehe 192 ki te 0.0001 mā te whakarea 192 ki te tau huripoki o 0.0001.

$$x^{2}+10000x=1920000$$

Whakawehea te 10000, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 5000. Nā, tāpiria te pūrua o te 5000 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+10000x+5000^{2}=1920000+5000^{2}$$

Pūrua 5000.

$$x^{2}+10000x+25000000=1920000+25000000$$

Tāpiri 1920000 ki te 25000000.

$$x^{2}+10000x+25000000=26920000$$

Tauwehea x^{2}+10000x+25000000. 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}.

$$\left(x+5000\right)^{2}=26920000$$

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

$$\sqrt{\left(x+5000\right)^{2}}=\sqrt{26920000}$$

Whakarūnātia.

$$x+5000=200\sqrt{673} x+5000=-200\sqrt{673}$$

Me tango 5000 mai i ngā taha e rua o te whārite.

$$x=200\sqrt{673}-5000 x=-200\sqrt{673}-5000$$