Whakaoti i te 0=y^2-14y

$$0 = y ^ { 2 } - 14 y$$

Whakaoti mō y

$$y=14$$

$$y=0$$

Ngā Upane Whakamahi Tauwehe

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$y^{2}-14y=0$$

Tauwehea te y.

$$y\left(y-14\right)=0$$

Hei kimi otinga whārite, me whakaoti te y=0 me te y-14=0.

$$y=0 y=14$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$y^{2}-14y=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -14 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-14\right)^{2}.

$$y=\frac{-\left(-14\right)±14}{2}$$

Ko te tauaro o -14 ko 14.

$$y=\frac{14±14}{2}$$

Nā, me whakaoti te whārite y=\frac{14±14}{2} ina he tāpiri te ±. Tāpiri 14 ki te 14.

$$y=\frac{28}{2}$$

Whakawehe 28 ki te 2.

$$y=14$$

Nā, me whakaoti te whārite y=\frac{14±14}{2} ina he tango te ±. Tango 14 mai i 14.

$$y=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$y=0$$

Kua oti te whārite te whakatau.

$$y=14 y=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$y^{2}-14y=0$$

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

$$y^{2}-14y+\left(-7\right)^{2}=\left(-7\right)^{2}$$

Pūrua -7.

$$y^{2}-14y+49=49$$

Tauwehea y^{2}-14y+49. 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}.

$$\left(y-7\right)^{2}=49$$

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

$$\sqrt{\left(y-7\right)^{2}}=\sqrt{49}$$

Whakarūnātia.

$$y-7=7 y-7=-7$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$y=14 y=0$$