Whakaoti i te x^2=25x

$$x ^ { 2 } = 25 x$$

Whakaoti mō x

$$x=25$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 25x mai i ngā taha e rua.

$$x^{2}-25x=0$$

Tauwehea te x.

$$x\left(x-25\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x-25=0.

$$x=0 x=25$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 25x mai i ngā taha e rua.

$$x^{2}-25x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -25 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-25\right)^{2}.

$$x=\frac{-\left(-25\right)±25}{2}$$

Ko te tauaro o -25 ko 25.

$$x=\frac{25±25}{2}$$

Nā, me whakaoti te whārite x=\frac{25±25}{2} ina he tāpiri te ±. Tāpiri 25 ki te 25.

$$x=\frac{50}{2}$$

Whakawehe 50 ki te 2.

$$x=25$$

Nā, me whakaoti te whārite x=\frac{25±25}{2} ina he tango te ±. Tango 25 mai i 25.

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

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=25 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 25x mai i ngā taha e rua.

$$x^{2}-25x=0$$

Whakawehea te -25, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{25}{2}. Nā, tāpiria te pūrua o te -\frac{25}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-25x+\left(-\frac{25}{2}\right)^{2}=\left(-\frac{25}{2}\right)^{2}$$

Pūruatia -\frac{25}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-25x+\frac{625}{4}=\frac{625}{4}$$

Tauwehea x^{2}-25x+\frac{625}{4}. 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}.

$$\left(x-\frac{25}{2}\right)^{2}=\frac{625}{4}$$

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

$$\sqrt{\left(x-\frac{25}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Whakarūnātia.

$$x-\frac{25}{2}=\frac{25}{2} x-\frac{25}{2}=-\frac{25}{2}$$

Me tāpiri \frac{25}{2} ki ngā taha e rua o te whārite.

$$x=25 x=0$$