Whakaoti i te 0=-6/25x^2+12/5x

$$0 = - \frac { 6 } { 25 } x ^ { 2 } + \frac { 12 } { 5 } x$$

Whakaoti mō x

$$x=10$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$-\frac{6}{25}x^{2}+\frac{12}{5}x=0$$

Tauwehea te x.

$$x\left(-\frac{6}{25}x+\frac{12}{5}\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -\frac{6x}{25}+\frac{12}{5}=0.

$$x=0 x=10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$-\frac{6}{25}x^{2}+\frac{12}{5}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{6}{25} mō a, \frac{12}{5} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{12}{5}±\sqrt{\left(\frac{12}{5}\right)^{2}}}{2\left(-\frac{6}{25}\right)}$$

Tuhia te pūtakerua o te \left(\frac{12}{5}\right)^{2}.

$$x=\frac{-\frac{12}{5}±\frac{12}{5}}{2\left(-\frac{6}{25}\right)}$$

Whakareatia 2 ki te -\frac{6}{25}.

$$x=\frac{-\frac{12}{5}±\frac{12}{5}}{-\frac{12}{25}}$$

Nā, me whakaoti te whārite x=\frac{-\frac{12}{5}±\frac{12}{5}}{-\frac{12}{25}} ina he tāpiri te ±. Tāpiri -\frac{12}{5} ki te \frac{12}{5} 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.

$$x=\frac{0}{-\frac{12}{25}}$$

Whakawehe 0 ki te -\frac{12}{25} mā te whakarea 0 ki te tau huripoki o -\frac{12}{25}.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-\frac{12}{5}±\frac{12}{5}}{-\frac{12}{25}} ina he tango te ±. Tango \frac{12}{5} mai i -\frac{12}{5} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{\frac{24}{5}}{-\frac{12}{25}}$$

Whakawehe -\frac{24}{5} ki te -\frac{12}{25} mā te whakarea -\frac{24}{5} ki te tau huripoki o -\frac{12}{25}.

$$x=10$$

Kua oti te whārite te whakatau.

$$x=0 x=10$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$-\frac{6}{25}x^{2}+\frac{12}{5}x=0$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{6}{25}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-\frac{6}{25}x^{2}+\frac{12}{5}x}{-\frac{6}{25}}=\frac{0}{-\frac{6}{25}}$$

Mā te whakawehe ki te -\frac{6}{25} ka wetekia te whakareanga ki te -\frac{6}{25}.

$$x^{2}+\frac{\frac{12}{5}}{-\frac{6}{25}}x=\frac{0}{-\frac{6}{25}}$$

Whakawehe \frac{12}{5} ki te -\frac{6}{25} mā te whakarea \frac{12}{5} ki te tau huripoki o -\frac{6}{25}.

$$x^{2}-10x=\frac{0}{-\frac{6}{25}}$$

Whakawehe 0 ki te -\frac{6}{25} mā te whakarea 0 ki te tau huripoki o -\frac{6}{25}.

$$x^{2}-10x=0$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-10x+\left(-5\right)^{2}=\left(-5\right)^{2}$$

Pūrua -5.

$$x^{2}-10x+25=25$$

Tauwehea x^{2}-10x+25. 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}.

$$\left(x-5\right)^{2}=25$$

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

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$x-5=5 x-5=-5$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=10 x=0$$