Whakaoti i te 100x^2+8x+6*3^2=5833

$$100 x ^ { 2 } + 8 x + 6 \cdot 3 ^ { 2 } = 5833$$

Whakaoti mō x

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25}\approx 7.562078663$$

$$x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}\approx -7.642078663$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$100x^{2}+8x+6\times 9=5833$$

Whakareatia te 6 ki te 9, ka 54.

$$100x^{2}+8x+54=5833$$

Tangohia te 5833 mai i ngā taha e rua.

$$100x^{2}+8x+54-5833=0$$

Tangohia te 5833 i te 54, ka -5779.

$$100x^{2}+8x-5779=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 100 mō a, 8 mō b, me -5779 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 100\left(-5779\right)}}{2\times 100}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 100\left(-5779\right)}}{2\times 100}$$

Whakareatia -4 ki te 100.

$$x=\frac{-8±\sqrt{64-400\left(-5779\right)}}{2\times 100}$$

Whakareatia -400 ki te -5779.

$$x=\frac{-8±\sqrt{64+2311600}}{2\times 100}$$

Tāpiri 64 ki te 2311600.

$$x=\frac{-8±\sqrt{2311664}}{2\times 100}$$

Tuhia te pūtakerua o te 2311664.

$$x=\frac{-8±4\sqrt{144479}}{2\times 100}$$

Whakareatia 2 ki te 100.

$$x=\frac{-8±4\sqrt{144479}}{200}$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{144479}}{200} ina he tāpiri te ±. Tāpiri -8 ki te 4\sqrt{144479}.

$$x=\frac{4\sqrt{144479}-8}{200}$$

Whakawehe -8+4\sqrt{144479} ki te 200.

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25}$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{144479}}{200} ina he tango te ±. Tango 4\sqrt{144479} mai i -8.

$$x=\frac{-4\sqrt{144479}-8}{200}$$

Whakawehe -8-4\sqrt{144479} ki te 200.

$$x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25} x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$100x^{2}+8x+6\times 9=5833$$

Whakareatia te 6 ki te 9, ka 54.

$$100x^{2}+8x+54=5833$$

Tangohia te 54 mai i ngā taha e rua.

$$100x^{2}+8x=5833-54$$

Tangohia te 54 i te 5833, ka 5779.

$$100x^{2}+8x=5779$$

Whakawehea ngā taha e rua ki te 100.

$$\frac{100x^{2}+8x}{100}=\frac{5779}{100}$$

Mā te whakawehe ki te 100 ka wetekia te whakareanga ki te 100.

$$x^{2}+\frac{8}{100}x=\frac{5779}{100}$$

Whakahekea te hautanga \frac{8}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}+\frac{2}{25}x=\frac{5779}{100}$$

Whakawehea te \frac{2}{25}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{25}. Nā, tāpiria te pūrua o te \frac{1}{25} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{2}{25}x+\left(\frac{1}{25}\right)^{2}=\frac{5779}{100}+\left(\frac{1}{25}\right)^{2}$$

Pūruatia \frac{1}{25} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{2}{25}x+\frac{1}{625}=\frac{5779}{100}+\frac{1}{625}$$

Tāpiri \frac{5779}{100} ki te \frac{1}{625} 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.

$$x^{2}+\frac{2}{25}x+\frac{1}{625}=\frac{144479}{2500}$$

Tauwehea x^{2}+\frac{2}{25}x+\frac{1}{625}. 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}.

$$\left(x+\frac{1}{25}\right)^{2}=\frac{144479}{2500}$$

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

$$\sqrt{\left(x+\frac{1}{25}\right)^{2}}=\sqrt{\frac{144479}{2500}}$$

Whakarūnātia.

$$x+\frac{1}{25}=\frac{\sqrt{144479}}{50} x+\frac{1}{25}=-\frac{\sqrt{144479}}{50}$$

Me tango \frac{1}{25} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25} x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}$$