Whakaoti i te 0.03=100x-41666.662x^2

$$0.03 = 100 x - 41666.662 x ^ { 2 }$$

Whakaoti mō x

$$x=\frac{17\sqrt{1081315}+25000}{20833331}\approx 0.002048528$$

$$x=\frac{25000-17\sqrt{1081315}}{20833331}\approx 0.000351472$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$100x-41666.662x^{2}=0.03$$

Tangohia te 0.03 mai i ngā taha e rua.

$$100x-41666.662x^{2}-0.03=0$$

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.

$$-41666.662x^{2}+100x-0.03=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -41666.662 mō a, 100 mō b, me -0.03 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-41666.662\right)\left(-0.03\right)}}{2\left(-41666.662\right)}$$

Pūrua 100.

$$x=\frac{-100±\sqrt{10000-4\left(-41666.662\right)\left(-0.03\right)}}{2\left(-41666.662\right)}$$

Whakareatia -4 ki te -41666.662.

$$x=\frac{-100±\sqrt{10000+166666.648\left(-0.03\right)}}{2\left(-41666.662\right)}$$

Whakareatia 166666.648 ki te -0.03 mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-100±\sqrt{10000-4999.99944}}{2\left(-41666.662\right)}$$

Tāpiri 10000 ki te -4999.99944.

$$x=\frac{-100±\sqrt{5000.00056}}{2\left(-41666.662\right)}$$

Tuhia te pūtakerua o te 5000.00056.

$$x=\frac{-100±\frac{17\sqrt{1081315}}{250}}{2\left(-41666.662\right)}$$

Whakareatia 2 ki te -41666.662.

$$x=\frac{-100±\frac{17\sqrt{1081315}}{250}}{-83333.324}$$

Nā, me whakaoti te whārite x=\frac{-100±\frac{17\sqrt{1081315}}{250}}{-83333.324} ina he tāpiri te ±. Tāpiri -100 ki te \frac{17\sqrt{1081315}}{250}.

$$x=\frac{\frac{17\sqrt{1081315}}{250}-100}{-83333.324}$$

Whakawehe -100+\frac{17\sqrt{1081315}}{250} ki te -83333.324 mā te whakarea -100+\frac{17\sqrt{1081315}}{250} ki te tau huripoki o -83333.324.

$$x=\frac{25000-17\sqrt{1081315}}{20833331}$$

Nā, me whakaoti te whārite x=\frac{-100±\frac{17\sqrt{1081315}}{250}}{-83333.324} ina he tango te ±. Tango \frac{17\sqrt{1081315}}{250} mai i -100.

$$x=\frac{-\frac{17\sqrt{1081315}}{250}-100}{-83333.324}$$

Whakawehe -100-\frac{17\sqrt{1081315}}{250} ki te -83333.324 mā te whakarea -100-\frac{17\sqrt{1081315}}{250} ki te tau huripoki o -83333.324.

$$x=\frac{17\sqrt{1081315}+25000}{20833331}$$

Kua oti te whārite te whakatau.

$$x=\frac{25000-17\sqrt{1081315}}{20833331} x=\frac{17\sqrt{1081315}+25000}{20833331}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$100x-41666.662x^{2}=0.03$$

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.

$$-41666.662x^{2}+100x=0.03$$

Whakawehea ngā taha e rua o te whārite ki te -41666.662, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-41666.662x^{2}+100x}{-41666.662}=\frac{0.03}{-41666.662}$$

Mā te whakawehe ki te -41666.662 ka wetekia te whakareanga ki te -41666.662.

$$x^{2}+\frac{100}{-41666.662}x=\frac{0.03}{-41666.662}$$

Whakawehe 100 ki te -41666.662 mā te whakarea 100 ki te tau huripoki o -41666.662.

$$x^{2}-\frac{50000}{20833331}x=\frac{0.03}{-41666.662}$$

Whakawehe 0.03 ki te -41666.662 mā te whakarea 0.03 ki te tau huripoki o -41666.662.

$$x^{2}-\frac{50000}{20833331}x=-\frac{15}{20833331}$$

Whakawehea te -\frac{50000}{20833331}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{25000}{20833331}. Nā, tāpiria te pūrua o te -\frac{25000}{20833331} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{50000}{20833331}x+\left(-\frac{25000}{20833331}\right)^{2}=-\frac{15}{20833331}+\left(-\frac{25000}{20833331}\right)^{2}$$

Pūruatia -\frac{25000}{20833331} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{50000}{20833331}x+\frac{625000000}{434027680555561}=-\frac{15}{20833331}+\frac{625000000}{434027680555561}$$

Tāpiri -\frac{15}{20833331} ki te \frac{625000000}{434027680555561} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{50000}{20833331}x+\frac{625000000}{434027680555561}=\frac{312500035}{434027680555561}$$

Tauwehea x^{2}-\frac{50000}{20833331}x+\frac{625000000}{434027680555561}. 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}.

$$\left(x-\frac{25000}{20833331}\right)^{2}=\frac{312500035}{434027680555561}$$

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

$$\sqrt{\left(x-\frac{25000}{20833331}\right)^{2}}=\sqrt{\frac{312500035}{434027680555561}}$$

Whakarūnātia.

$$x-\frac{25000}{20833331}=\frac{17\sqrt{1081315}}{20833331} x-\frac{25000}{20833331}=-\frac{17\sqrt{1081315}}{20833331}$$

Me tāpiri \frac{25000}{20833331} ki ngā taha e rua o te whārite.

$$x=\frac{17\sqrt{1081315}+25000}{20833331} x=\frac{25000-17\sqrt{1081315}}{20833331}$$