Whakaoti i te (3s-7)^2-49=0

$$( 3 s - 7 ) ^ { 2 } - 49 = 0$$

Whakaoti mō s

$$s = \frac{14}{3} = 4\frac{2}{3} \approx 4.666666667$$

$$s=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(3s-7\right)^{2}.

$$9s^{2}-42s+49-49=0$$

Tangohia te 49 i te 49, ka 0.

$$9s^{2}-42s=0$$

Tauwehea te s.

$$s\left(9s-42\right)=0$$

Hei kimi otinga whārite, me whakaoti te s=0 me te 9s-42=0.

$$s=0 s=\frac{14}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(3s-7\right)^{2}.

$$9s^{2}-42s+49-49=0$$

Tangohia te 49 i te 49, ka 0.

$$9s^{2}-42s=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, -42 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\left(-42\right)±\sqrt{\left(-42\right)^{2}}}{2\times 9}$$

Tuhia te pūtakerua o te \left(-42\right)^{2}.

$$s=\frac{-\left(-42\right)±42}{2\times 9}$$

Ko te tauaro o -42 ko 42.

$$s=\frac{42±42}{2\times 9}$$

Whakareatia 2 ki te 9.

$$s=\frac{42±42}{18}$$

Nā, me whakaoti te whārite s=\frac{42±42}{18} ina he tāpiri te ±. Tāpiri 42 ki te 42.

$$s=\frac{84}{18}$$

Whakahekea te hautanga \frac{84}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$s=\frac{14}{3}$$

Nā, me whakaoti te whārite s=\frac{42±42}{18} ina he tango te ±. Tango 42 mai i 42.

$$s=\frac{0}{18}$$

Whakawehe 0 ki te 18.

$$s=0$$

Kua oti te whārite te whakatau.

$$s=\frac{14}{3} s=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(3s-7\right)^{2}.

$$9s^{2}-42s+49-49=0$$

Tangohia te 49 i te 49, ka 0.

$$9s^{2}-42s=0$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9s^{2}-42s}{9}=\frac{0}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$s^{2}+\left(-\frac{42}{9}\right)s=\frac{0}{9}$$

Whakahekea te hautanga \frac{-42}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$s^{2}-\frac{14}{3}s=\frac{0}{9}$$

Whakawehe 0 ki te 9.

$$s^{2}-\frac{14}{3}s=0$$

Whakawehea te -\frac{14}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{3}. Nā, tāpiria te pūrua o te -\frac{7}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$s^{2}-\frac{14}{3}s+\left(-\frac{7}{3}\right)^{2}=\left(-\frac{7}{3}\right)^{2}$$

Pūruatia -\frac{7}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$s^{2}-\frac{14}{3}s+\frac{49}{9}=\frac{49}{9}$$

Tauwehea s^{2}-\frac{14}{3}s+\frac{49}{9}. 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}.

$$\left(s-\frac{7}{3}\right)^{2}=\frac{49}{9}$$

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

$$\sqrt{\left(s-\frac{7}{3}\right)^{2}}=\sqrt{\frac{49}{9}}$$

Whakarūnātia.

$$s-\frac{7}{3}=\frac{7}{3} s-\frac{7}{3}=-\frac{7}{3}$$

Me tāpiri \frac{7}{3} ki ngā taha e rua o te whārite.

$$s=\frac{14}{3} s=0$$