Whakaoti i te 0=0.75x-0.020x^2

$$0=0.75x-0.020 { x }^{ 2 }$$

Whakaoti mō x

$$x=37.5$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$0.75x-0.02x^{2}=0$$

Tauwehea te x.

$$x\left(0.75-0.02x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 0.75-\frac{x}{50}=0.

$$x=0 x=\frac{75}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$0.75x-0.02x^{2}=0$$

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.

$$-0.02x^{2}+0.75x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -0.02 mō a, 0.75 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.75±\sqrt{0.75^{2}}}{2\left(-0.02\right)}$$

Tuhia te pūtakerua o te 0.75^{2}.

$$x=\frac{-0.75±\frac{3}{4}}{2\left(-0.02\right)}$$

Whakareatia 2 ki te -0.02.

$$x=\frac{-0.75±\frac{3}{4}}{-0.04}$$

Nā, me whakaoti te whārite x=\frac{-0.75±\frac{3}{4}}{-0.04} ina he tāpiri te ±. Tāpiri -0.75 ki te \frac{3}{4} 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.

$$x=\frac{0}{-0.04}$$

Whakawehe 0 ki te -0.04 mā te whakarea 0 ki te tau huripoki o -0.04.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-0.75±\frac{3}{4}}{-0.04} ina he tango te ±. Tango \frac{3}{4} mai i -0.75 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.

$$x=-\frac{\frac{3}{2}}{-0.04}$$

Whakawehe -\frac{3}{2} ki te -0.04 mā te whakarea -\frac{3}{2} ki te tau huripoki o -0.04.

$$x=\frac{75}{2}$$

Kua oti te whārite te whakatau.

$$x=0 x=\frac{75}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$0.75x-0.02x^{2}=0$$

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.

$$-0.02x^{2}+0.75x=0$$

Me whakarea ngā taha e rua ki te -50.

$$\frac{-0.02x^{2}+0.75x}{-0.02}=\frac{0}{-0.02}$$

Mā te whakawehe ki te -0.02 ka wetekia te whakareanga ki te -0.02.

$$x^{2}+\frac{0.75}{-0.02}x=\frac{0}{-0.02}$$

Whakawehe 0.75 ki te -0.02 mā te whakarea 0.75 ki te tau huripoki o -0.02.

$$x^{2}-37.5x=\frac{0}{-0.02}$$

Whakawehe 0 ki te -0.02 mā te whakarea 0 ki te tau huripoki o -0.02.

$$x^{2}-37.5x=0$$

Whakawehea te -37.5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -18.75. Nā, tāpiria te pūrua o te -18.75 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-37.5x+\left(-18.75\right)^{2}=\left(-18.75\right)^{2}$$

Pūruatia -18.75 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-37.5x+351.5625=351.5625$$

Tauwehea x^{2}-37.5x+351.5625. 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}.

$$\left(x-18.75\right)^{2}=351.5625$$

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

$$\sqrt{\left(x-18.75\right)^{2}}=\sqrt{351.5625}$$

Whakarūnātia.

$$x-18.75=\frac{75}{4} x-18.75=-\frac{75}{4}$$

Me tāpiri 18.75 ki ngā taha e rua o te whārite.

$$x=\frac{75}{2} x=0$$