Whakaoti i te 301x^2-918x=256

$$301 x ^ { 2 } - 918 x = 256$$

Whakaoti mō x

$$x = \frac{\sqrt{287737} + 459}{301} \approx 3.307014029$$

$$x=\frac{459-\sqrt{287737}}{301}\approx -0.257180142$$

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.

$$301x^{2}-918x=256$$

Me tango 256 mai i ngā taha e rua o te whārite.

$$301x^{2}-918x-256=256-256$$

Mā te tango i te 256 i a ia ake anō ka toe ko te 0.

$$301x^{2}-918x-256=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 301 mō a, -918 mō b, me -256 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-918\right)±\sqrt{\left(-918\right)^{2}-4\times 301\left(-256\right)}}{2\times 301}$$

Pūrua -918.

$$x=\frac{-\left(-918\right)±\sqrt{842724-4\times 301\left(-256\right)}}{2\times 301}$$

Whakareatia -4 ki te 301.

$$x=\frac{-\left(-918\right)±\sqrt{842724-1204\left(-256\right)}}{2\times 301}$$

Whakareatia -1204 ki te -256.

$$x=\frac{-\left(-918\right)±\sqrt{842724+308224}}{2\times 301}$$

Tāpiri 842724 ki te 308224.

$$x=\frac{-\left(-918\right)±\sqrt{1150948}}{2\times 301}$$

Tuhia te pūtakerua o te 1150948.

$$x=\frac{-\left(-918\right)±2\sqrt{287737}}{2\times 301}$$

Ko te tauaro o -918 ko 918.

$$x=\frac{918±2\sqrt{287737}}{2\times 301}$$

Whakareatia 2 ki te 301.

$$x=\frac{918±2\sqrt{287737}}{602}$$

Nā, me whakaoti te whārite x=\frac{918±2\sqrt{287737}}{602} ina he tāpiri te ±. Tāpiri 918 ki te 2\sqrt{287737}.

$$x=\frac{2\sqrt{287737}+918}{602}$$

Whakawehe 918+2\sqrt{287737} ki te 602.

$$x=\frac{\sqrt{287737}+459}{301}$$

Nā, me whakaoti te whārite x=\frac{918±2\sqrt{287737}}{602} ina he tango te ±. Tango 2\sqrt{287737} mai i 918.

$$x=\frac{918-2\sqrt{287737}}{602}$$

Whakawehe 918-2\sqrt{287737} ki te 602.

$$x=\frac{459-\sqrt{287737}}{301}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{287737}+459}{301} x=\frac{459-\sqrt{287737}}{301}$$

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.

$$301x^{2}-918x=256$$

Whakawehea ngā taha e rua ki te 301.

$$\frac{301x^{2}-918x}{301}=\frac{256}{301}$$

Mā te whakawehe ki te 301 ka wetekia te whakareanga ki te 301.

$$x^{2}-\frac{918}{301}x=\frac{256}{301}$$

Whakawehea te -\frac{918}{301}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{459}{301}. Nā, tāpiria te pūrua o te -\frac{459}{301} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{918}{301}x+\left(-\frac{459}{301}\right)^{2}=\frac{256}{301}+\left(-\frac{459}{301}\right)^{2}$$

Pūruatia -\frac{459}{301} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{918}{301}x+\frac{210681}{90601}=\frac{256}{301}+\frac{210681}{90601}$$

Tāpiri \frac{256}{301} ki te \frac{210681}{90601} 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.

$$x^{2}-\frac{918}{301}x+\frac{210681}{90601}=\frac{287737}{90601}$$

Tauwehea x^{2}-\frac{918}{301}x+\frac{210681}{90601}. 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}.

$$\left(x-\frac{459}{301}\right)^{2}=\frac{287737}{90601}$$

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

$$\sqrt{\left(x-\frac{459}{301}\right)^{2}}=\sqrt{\frac{287737}{90601}}$$

Whakarūnātia.

$$x-\frac{459}{301}=\frac{\sqrt{287737}}{301} x-\frac{459}{301}=-\frac{\sqrt{287737}}{301}$$

Me tāpiri \frac{459}{301} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{287737}+459}{301} x=\frac{459-\sqrt{287737}}{301}$$