Whakaoti i te 900x^2-136x+4=0

$$900 { x }^{ 2 } -136x+4=0$$

Whakaoti mō x

$$x=\frac{1}{25}=0.04$$

$$x=\frac{1}{9}\approx 0.111111111$$

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.

$$900x^{2}-136x+4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 900 mō a, -136 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-136\right)±\sqrt{\left(-136\right)^{2}-4\times 900\times 4}}{2\times 900}$$

Pūrua -136.

$$x=\frac{-\left(-136\right)±\sqrt{18496-4\times 900\times 4}}{2\times 900}$$

Whakareatia -4 ki te 900.

$$x=\frac{-\left(-136\right)±\sqrt{18496-3600\times 4}}{2\times 900}$$

Whakareatia -3600 ki te 4.

$$x=\frac{-\left(-136\right)±\sqrt{18496-14400}}{2\times 900}$$

Tāpiri 18496 ki te -14400.

$$x=\frac{-\left(-136\right)±\sqrt{4096}}{2\times 900}$$

Tuhia te pūtakerua o te 4096.

$$x=\frac{-\left(-136\right)±64}{2\times 900}$$

Ko te tauaro o -136 ko 136.

$$x=\frac{136±64}{2\times 900}$$

Whakareatia 2 ki te 900.

$$x=\frac{136±64}{1800}$$

Nā, me whakaoti te whārite x=\frac{136±64}{1800} ina he tāpiri te ±. Tāpiri 136 ki te 64.

$$x=\frac{200}{1800}$$

Whakahekea te hautanga \frac{200}{1800} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 200.

$$x=\frac{1}{9}$$

Nā, me whakaoti te whārite x=\frac{136±64}{1800} ina he tango te ±. Tango 64 mai i 136.

$$x=\frac{72}{1800}$$

Whakahekea te hautanga \frac{72}{1800} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 72.

$$x=\frac{1}{25}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{9} x=\frac{1}{25}$$

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.

$$900x^{2}-136x+4=0$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$900x^{2}-136x+4-4=-4$$

Mā te tango i te 4 i a ia ake anō ka toe ko te 0.

$$900x^{2}-136x=-4$$

Whakawehea ngā taha e rua ki te 900.

$$\frac{900x^{2}-136x}{900}=-\frac{4}{900}$$

Mā te whakawehe ki te 900 ka wetekia te whakareanga ki te 900.

$$x^{2}+\left(-\frac{136}{900}\right)x=-\frac{4}{900}$$

Whakahekea te hautanga \frac{-136}{900} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{34}{225}x=-\frac{4}{900}$$

Whakahekea te hautanga \frac{-4}{900} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{34}{225}x=-\frac{1}{225}$$

Whakawehea te -\frac{34}{225}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{17}{225}. Nā, tāpiria te pūrua o te -\frac{17}{225} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{34}{225}x+\left(-\frac{17}{225}\right)^{2}=-\frac{1}{225}+\left(-\frac{17}{225}\right)^{2}$$

Pūruatia -\frac{17}{225} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{34}{225}x+\frac{289}{50625}=-\frac{1}{225}+\frac{289}{50625}$$

Tāpiri -\frac{1}{225} ki te \frac{289}{50625} 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.

$$x^{2}-\frac{34}{225}x+\frac{289}{50625}=\frac{64}{50625}$$

Tauwehea x^{2}-\frac{34}{225}x+\frac{289}{50625}. 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}.

$$\left(x-\frac{17}{225}\right)^{2}=\frac{64}{50625}$$

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

$$\sqrt{\left(x-\frac{17}{225}\right)^{2}}=\sqrt{\frac{64}{50625}}$$

Whakarūnātia.

$$x-\frac{17}{225}=\frac{8}{225} x-\frac{17}{225}=-\frac{8}{225}$$

Me tāpiri \frac{17}{225} ki ngā taha e rua o te whārite.

$$x=\frac{1}{9} x=\frac{1}{25}$$