Whakaoti i te 2v(v-7)=5v(v-7)

$$2 v ( v - 7 ) = 5 v ( v - 7 )$$

Whakaoti mō v

$$v=7$$

$$v=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 2v ki te v-7.

$$2v^{2}-14v=5v\left(v-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5v ki te v-7.

$$2v^{2}-14v=5v^{2}-35v$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$2v^{2}-14v-5v^{2}=-35v$$

Pahekotia te 2v^{2} me -5v^{2}, ka -3v^{2}.

$$-3v^{2}-14v=-35v$$

Me tāpiri te 35v ki ngā taha e rua.

$$-3v^{2}-14v+35v=0$$

Pahekotia te -14v me 35v, ka 21v.

$$-3v^{2}+21v=0$$

Tauwehea te v.

$$v\left(-3v+21\right)=0$$

Hei kimi otinga whārite, me whakaoti te v=0 me te -3v+21=0.

$$v=0 v=7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2v ki te v-7.

$$2v^{2}-14v=5v\left(v-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5v ki te v-7.

$$2v^{2}-14v=5v^{2}-35v$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$2v^{2}-14v-5v^{2}=-35v$$

Pahekotia te 2v^{2} me -5v^{2}, ka -3v^{2}.

$$-3v^{2}-14v=-35v$$

Me tāpiri te 35v ki ngā taha e rua.

$$-3v^{2}-14v+35v=0$$

Pahekotia te -14v me 35v, ka 21v.

$$-3v^{2}+21v=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 21 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-21±\sqrt{21^{2}}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 21^{2}.

$$v=\frac{-21±21}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$v=\frac{-21±21}{-6}$$

Nā, me whakaoti te whārite v=\frac{-21±21}{-6} ina he tāpiri te ±. Tāpiri -21 ki te 21.

$$v=\frac{0}{-6}$$

Whakawehe 0 ki te -6.

$$v=0$$

Nā, me whakaoti te whārite v=\frac{-21±21}{-6} ina he tango te ±. Tango 21 mai i -21.

$$v=-\frac{42}{-6}$$

Whakawehe -42 ki te -6.

$$v=7$$

Kua oti te whārite te whakatau.

$$v=0 v=7$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2v ki te v-7.

$$2v^{2}-14v=5v\left(v-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5v ki te v-7.

$$2v^{2}-14v=5v^{2}-35v$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$2v^{2}-14v-5v^{2}=-35v$$

Pahekotia te 2v^{2} me -5v^{2}, ka -3v^{2}.

$$-3v^{2}-14v=-35v$$

Me tāpiri te 35v ki ngā taha e rua.

$$-3v^{2}-14v+35v=0$$

Pahekotia te -14v me 35v, ka 21v.

$$-3v^{2}+21v=0$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3v^{2}+21v}{-3}=\frac{0}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$v^{2}+\frac{21}{-3}v=\frac{0}{-3}$$

Whakawehe 21 ki te -3.

$$v^{2}-7v=\frac{0}{-3}$$

Whakawehe 0 ki te -3.

$$v^{2}-7v=0$$

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

$$v^{2}-7v+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$v^{2}-7v+\frac{49}{4}=\frac{49}{4}$$

Tauwehea v^{2}-7v+\frac{49}{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}.

$$\left(v-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(v-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$v-\frac{7}{2}=\frac{7}{2} v-\frac{7}{2}=-\frac{7}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$v=7 v=0$$