Whakaoti i te 2x^2+3x-5x=0

$$2 x ^ { 2 } + 3 x - 5 x = 0$$

Whakaoti mō x

$$x=1$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(2x+3-5\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2x-2=0.

$$x=0 x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 3x me -5x, ka -2x.

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

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

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

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

$$x=\frac{-\left(-2\right)±2}{2\times 2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{2±2}{4}$$

Nā, me whakaoti te whārite x=\frac{2±2}{4} ina he tāpiri te ±. Tāpiri 2 ki te 2.

$$x=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{2±2}{4} ina he tango te ±. Tango 2 mai i 2.

$$x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=1 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 3x me -5x, ka -2x.

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

Whakawehea ngā taha e rua ki te 2.

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

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\left(-\frac{2}{2}\right)x=\frac{0}{2}$$

Whakawehe -2 ki te 2.

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

Whakawehe 0 ki te 2.

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

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-x+\frac{1}{4}=\frac{1}{4}$$

Tauwehea x^{2}-x+\frac{1}{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}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{1}{2} x-\frac{1}{2}=-\frac{1}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$x=1 x=0$$