Whakaoti i te 2.0365*695x^2-34xdiv365=5874/65

$$2.0365 \times 695 { x }^{ 2 } -34x \div 365= \frac{ 5874 }{ 65 }$$

Whakaoti mō x

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}\approx 0.252715711$$

$$x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}\approx -0.252649897$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 4745, arā, te tauraro pātahi he tino iti rawa te kitea o 365,65.

$$9663.1925\times 695x^{2}-13\times 34x=428802$$

Whakareatia te 9663.1925 ki te 695, ka 6715918.7875.

$$6715918.7875x^{2}-13\times 34x=428802$$

Whakareatia te -13 ki te 34, ka -442.

$$6715918.7875x^{2}-442x=428802$$

Tangohia te 428802 mai i ngā taha e rua.

$$6715918.7875x^{2}-442x-428802=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6715918.7875 mō a, -442 mō b, me -428802 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-442\right)±\sqrt{\left(-442\right)^{2}-4\times 6715918.7875\left(-428802\right)}}{2\times 6715918.7875}$$

Pūrua -442.

$$x=\frac{-\left(-442\right)±\sqrt{195364-4\times 6715918.7875\left(-428802\right)}}{2\times 6715918.7875}$$

Whakareatia -4 ki te 6715918.7875.

$$x=\frac{-\left(-442\right)±\sqrt{195364-26863675.15\left(-428802\right)}}{2\times 6715918.7875}$$

Whakareatia -26863675.15 ki te -428802.

$$x=\frac{-\left(-442\right)±\sqrt{195364+11519197631670.3}}{2\times 6715918.7875}$$

Tāpiri 195364 ki te 11519197631670.3.

$$x=\frac{-\left(-442\right)±\sqrt{11519197827034.3}}{2\times 6715918.7875}$$

Tuhia te pūtakerua o te 11519197827034.3.

$$x=\frac{-\left(-442\right)±\frac{\sqrt{1151919782703430}}{10}}{2\times 6715918.7875}$$

Ko te tauaro o -442 ko 442.

$$x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{2\times 6715918.7875}$$

Whakareatia 2 ki te 6715918.7875.

$$x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{13431837.575}$$

Nā, me whakaoti te whārite x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{13431837.575} ina he tāpiri te ±. Tāpiri 442 ki te \frac{\sqrt{1151919782703430}}{10}.

$$x=\frac{\frac{\sqrt{1151919782703430}}{10}+442}{13431837.575}$$

Whakawehe 442+\frac{\sqrt{1151919782703430}}{10} ki te 13431837.575 mā te whakarea 442+\frac{\sqrt{1151919782703430}}{10} ki te tau huripoki o 13431837.575.

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$

Nā, me whakaoti te whārite x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{13431837.575} ina he tango te ±. Tango \frac{\sqrt{1151919782703430}}{10} mai i 442.

$$x=\frac{-\frac{\sqrt{1151919782703430}}{10}+442}{13431837.575}$$

Whakawehe 442-\frac{\sqrt{1151919782703430}}{10} ki te 13431837.575 mā te whakarea 442-\frac{\sqrt{1151919782703430}}{10} ki te tau huripoki o 13431837.575.

$$x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$

Kua oti te whārite te whakatau.

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731} x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua o te whārite ki te 4745, arā, te tauraro pātahi he tino iti rawa te kitea o 365,65.

$$9663.1925\times 695x^{2}-13\times 34x=428802$$

Whakareatia te 9663.1925 ki te 695, ka 6715918.7875.

$$6715918.7875x^{2}-13\times 34x=428802$$

Whakareatia te -13 ki te 34, ka -442.

$$6715918.7875x^{2}-442x=428802$$

Whakawehea ngā taha e rua o te whārite ki te 6715918.7875, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{6715918.7875x^{2}-442x}{6715918.7875}=\frac{428802}{6715918.7875}$$

Mā te whakawehe ki te 6715918.7875 ka wetekia te whakareanga ki te 6715918.7875.

$$x^{2}+\left(-\frac{442}{6715918.7875}\right)x=\frac{428802}{6715918.7875}$$

Whakawehe -442 ki te 6715918.7875 mā te whakarea -442 ki te tau huripoki o 6715918.7875.

$$x^{2}-\frac{2720}{41328731}x=\frac{428802}{6715918.7875}$$

Whakawehe 428802 ki te 6715918.7875 mā te whakarea 428802 ki te tau huripoki o 6715918.7875.

$$x^{2}-\frac{2720}{41328731}x=\frac{469920}{7359911}$$

Whakawehea te -\frac{2720}{41328731}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1360}{41328731}. Nā, tāpiria te pūrua o te -\frac{1360}{41328731} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{2720}{41328731}x+\left(-\frac{1360}{41328731}\right)^{2}=\frac{469920}{7359911}+\left(-\frac{1360}{41328731}\right)^{2}$$

Pūruatia -\frac{1360}{41328731} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{2720}{41328731}x+\frac{1849600}{1708064006070361}=\frac{469920}{7359911}+\frac{1849600}{1708064006070361}$$

Tāpiri \frac{469920}{7359911} ki te \frac{1849600}{1708064006070361} 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.

$$x^{2}-\frac{2720}{41328731}x+\frac{1849600}{1708064006070361}=\frac{1417747424865760}{22204832078914693}$$

Tauwehea x^{2}-\frac{2720}{41328731}x+\frac{1849600}{1708064006070361}. 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}.

$$\left(x-\frac{1360}{41328731}\right)^{2}=\frac{1417747424865760}{22204832078914693}$$

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

$$\sqrt{\left(x-\frac{1360}{41328731}\right)^{2}}=\sqrt{\frac{1417747424865760}{22204832078914693}}$$

Whakarūnātia.

$$x-\frac{1360}{41328731}=\frac{4\sqrt{1151919782703430}}{537273503} x-\frac{1360}{41328731}=-\frac{4\sqrt{1151919782703430}}{537273503}$$

Me tāpiri \frac{1360}{41328731} ki ngā taha e rua o te whārite.

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731} x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$