Whakaoti i te 8s^2-13s=-3/2

$$8 s ^ { 2 } - 13 s = - \frac { 3 } { 2 }$$

Whakaoti mō s

$$s=\frac{1}{8}=0.125$$

$$s = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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.

$$8s^{2}-13s=-\frac{3}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$8s^{2}-13s-\left(-\frac{3}{2}\right)=-\frac{3}{2}-\left(-\frac{3}{2}\right)$$

Mā te tango i te -\frac{3}{2} i a ia ake anō ka toe ko te 0.

$$8s^{2}-13s-\left(-\frac{3}{2}\right)=0$$

Tango -\frac{3}{2} mai i 0.

$$8s^{2}-13s+\frac{3}{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -13 mō b, me \frac{3}{2} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 8\times \frac{3}{2}}}{2\times 8}$$

Pūrua -13.

$$s=\frac{-\left(-13\right)±\sqrt{169-4\times 8\times \frac{3}{2}}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$s=\frac{-\left(-13\right)±\sqrt{169-32\times \frac{3}{2}}}{2\times 8}$$

Whakareatia -32 ki te \frac{3}{2}.

$$s=\frac{-\left(-13\right)±\sqrt{169-48}}{2\times 8}$$

Tāpiri 169 ki te -48.

$$s=\frac{-\left(-13\right)±\sqrt{121}}{2\times 8}$$

Tuhia te pūtakerua o te 121.

$$s=\frac{-\left(-13\right)±11}{2\times 8}$$

Ko te tauaro o -13 ko 13.

$$s=\frac{13±11}{2\times 8}$$

Whakareatia 2 ki te 8.

$$s=\frac{13±11}{16}$$

Nā, me whakaoti te whārite s=\frac{13±11}{16} ina he tāpiri te ±. Tāpiri 13 ki te 11.

$$s=\frac{24}{16}$$

Whakahekea te hautanga \frac{24}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$s=\frac{3}{2}$$

Nā, me whakaoti te whārite s=\frac{13±11}{16} ina he tango te ±. Tango 11 mai i 13.

$$s=\frac{2}{16}$$

Whakahekea te hautanga \frac{2}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$s=\frac{1}{8}$$

Kua oti te whārite te whakatau.

$$s=\frac{3}{2} s=\frac{1}{8}$$

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.

$$8s^{2}-13s=-\frac{3}{2}$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8s^{2}-13s}{8}=-\frac{\frac{3}{2}}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$s^{2}-\frac{13}{8}s=-\frac{\frac{3}{2}}{8}$$

Whakawehe -\frac{3}{2} ki te 8.

$$s^{2}-\frac{13}{8}s=-\frac{3}{16}$$

Whakawehea te -\frac{13}{8}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{16}. Nā, tāpiria te pūrua o te -\frac{13}{16} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$s^{2}-\frac{13}{8}s+\left(-\frac{13}{16}\right)^{2}=-\frac{3}{16}+\left(-\frac{13}{16}\right)^{2}$$

Pūruatia -\frac{13}{16} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$s^{2}-\frac{13}{8}s+\frac{169}{256}=-\frac{3}{16}+\frac{169}{256}$$

Tāpiri -\frac{3}{16} ki te \frac{169}{256} 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.

$$s^{2}-\frac{13}{8}s+\frac{169}{256}=\frac{121}{256}$$

Tauwehea s^{2}-\frac{13}{8}s+\frac{169}{256}. 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}.

$$\left(s-\frac{13}{16}\right)^{2}=\frac{121}{256}$$

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

$$\sqrt{\left(s-\frac{13}{16}\right)^{2}}=\sqrt{\frac{121}{256}}$$

Whakarūnātia.

$$s-\frac{13}{16}=\frac{11}{16} s-\frac{13}{16}=-\frac{11}{16}$$

Me tāpiri \frac{13}{16} ki ngā taha e rua o te whārite.

$$s=\frac{3}{2} s=\frac{1}{8}$$