Whakaoti i te 0.0149x^2+8.134x=2624.67

$$0.0149 x ^ { 2 } + 8.134 x = 2624.67$$

Whakaoti mō x

$$x = \frac{20 \sqrt{13912018} - 40670}{149} \approx 227.70225068$$

$$x=\frac{-20\sqrt{13912018}-40670}{149}\approx -773.608290948$$

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.

$$0.0149x^{2}+8.134x=2624.67$$

Me tango 2624.67 mai i ngā taha e rua o te whārite.

$$0.0149x^{2}+8.134x-2624.67=2624.67-2624.67$$

Mā te tango i te 2624.67 i a ia ake anō ka toe ko te 0.

$$0.0149x^{2}+8.134x-2624.67=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.0149 mō a, 8.134 mō b, me -2624.67 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8.134±\sqrt{8.134^{2}-4\times 0.0149\left(-2624.67\right)}}{2\times 0.0149}$$

Pūruatia 8.134 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-8.134±\sqrt{66.161956-4\times 0.0149\left(-2624.67\right)}}{2\times 0.0149}$$

Whakareatia -4 ki te 0.0149.

$$x=\frac{-8.134±\sqrt{66.161956-0.0596\left(-2624.67\right)}}{2\times 0.0149}$$

Whakareatia -0.0596 ki te -2624.67 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.

$$x=\frac{-8.134±\sqrt{\frac{16540489+39107583}{250000}}}{2\times 0.0149}$$

Tāpiri 66.161956 ki te 156.430332 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.

$$x=\frac{-8.134±\sqrt{222.592288}}{2\times 0.0149}$$

Tuhia te pūtakerua o te 222.592288.

$$x=\frac{-8.134±\frac{\sqrt{13912018}}{250}}{2\times 0.0149}$$

Whakareatia 2 ki te 0.0149.

$$x=\frac{-8.134±\frac{\sqrt{13912018}}{250}}{0.0298}$$

Nā, me whakaoti te whārite x=\frac{-8.134±\frac{\sqrt{13912018}}{250}}{0.0298} ina he tāpiri te ±. Tāpiri -8.134 ki te \frac{\sqrt{13912018}}{250}.

$$x=\frac{\frac{\sqrt{13912018}}{250}-\frac{4067}{500}}{0.0298}$$

Whakawehe -\frac{4067}{500}+\frac{\sqrt{13912018}}{250} ki te 0.0298 mā te whakarea -\frac{4067}{500}+\frac{\sqrt{13912018}}{250} ki te tau huripoki o 0.0298.

$$x=\frac{20\sqrt{13912018}-40670}{149}$$

Nā, me whakaoti te whārite x=\frac{-8.134±\frac{\sqrt{13912018}}{250}}{0.0298} ina he tango te ±. Tango \frac{\sqrt{13912018}}{250} mai i -8.134.

$$x=\frac{-\frac{\sqrt{13912018}}{250}-\frac{4067}{500}}{0.0298}$$

Whakawehe -\frac{4067}{500}-\frac{\sqrt{13912018}}{250} ki te 0.0298 mā te whakarea -\frac{4067}{500}-\frac{\sqrt{13912018}}{250} ki te tau huripoki o 0.0298.

$$x=\frac{-20\sqrt{13912018}-40670}{149}$$

Kua oti te whārite te whakatau.

$$x=\frac{20\sqrt{13912018}-40670}{149} x=\frac{-20\sqrt{13912018}-40670}{149}$$

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.

$$0.0149x^{2}+8.134x=2624.67$$

Whakawehea ngā taha e rua o te whārite ki te 0.0149, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{0.0149x^{2}+8.134x}{0.0149}=\frac{2624.67}{0.0149}$$

Mā te whakawehe ki te 0.0149 ka wetekia te whakareanga ki te 0.0149.

$$x^{2}+\frac{8.134}{0.0149}x=\frac{2624.67}{0.0149}$$

Whakawehe 8.134 ki te 0.0149 mā te whakarea 8.134 ki te tau huripoki o 0.0149.

$$x^{2}+\frac{81340}{149}x=\frac{2624.67}{0.0149}$$

Whakawehe 2624.67 ki te 0.0149 mā te whakarea 2624.67 ki te tau huripoki o 0.0149.

$$x^{2}+\frac{81340}{149}x=\frac{26246700}{149}$$

Whakawehea te \frac{81340}{149}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{40670}{149}. Nā, tāpiria te pūrua o te \frac{40670}{149} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{81340}{149}x+\frac{40670}{149}^{2}=\frac{26246700}{149}+\frac{40670}{149}^{2}$$

Pūruatia \frac{40670}{149} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{81340}{149}x+\frac{1654048900}{22201}=\frac{26246700}{149}+\frac{1654048900}{22201}$$

Tāpiri \frac{26246700}{149} ki te \frac{1654048900}{22201} 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.

$$x^{2}+\frac{81340}{149}x+\frac{1654048900}{22201}=\frac{5564807200}{22201}$$

Tauwehea x^{2}+\frac{81340}{149}x+\frac{1654048900}{22201}. 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}.

$$\left(x+\frac{40670}{149}\right)^{2}=\frac{5564807200}{22201}$$

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

$$\sqrt{\left(x+\frac{40670}{149}\right)^{2}}=\sqrt{\frac{5564807200}{22201}}$$

Whakarūnātia.

$$x+\frac{40670}{149}=\frac{20\sqrt{13912018}}{149} x+\frac{40670}{149}=-\frac{20\sqrt{13912018}}{149}$$

Me tango \frac{40670}{149} mai i ngā taha e rua o te whārite.

$$x=\frac{20\sqrt{13912018}-40670}{149} x=\frac{-20\sqrt{13912018}-40670}{149}$$