Whakaoti i te x=xleft(200+10(150-x)right)

$$x = x \left( 200+10(150-x) \right)$$

Whakaoti mō x

$$x = \frac{1699}{10} = 169\frac{9}{10} = 169.9$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 10 ki te 150-x.

$$x=x\left(200+1500-10x\right)$$

Tāpirihia te 200 ki te 1500, ka 1700.

$$x=x\left(1700-10x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 1700-10x.

$$x=1700x-10x^{2}$$

Tangohia te 1700x mai i ngā taha e rua.

$$x-1700x=-10x^{2}$$

Pahekotia te x me -1700x, ka -1699x.

$$-1699x=-10x^{2}$$

Me tāpiri te 10x^{2} ki ngā taha e rua.

$$-1699x+10x^{2}=0$$

Tauwehea te x.

$$x\left(-1699+10x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -1699+10x=0.

$$x=0 x=\frac{1699}{10}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 10 ki te 150-x.

$$x=x\left(200+1500-10x\right)$$

Tāpirihia te 200 ki te 1500, ka 1700.

$$x=x\left(1700-10x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 1700-10x.

$$x=1700x-10x^{2}$$

Tangohia te 1700x mai i ngā taha e rua.

$$x-1700x=-10x^{2}$$

Pahekotia te x me -1700x, ka -1699x.

$$-1699x=-10x^{2}$$

Me tāpiri te 10x^{2} ki ngā taha e rua.

$$-1699x+10x^{2}=0$$

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.

$$10x^{2}-1699x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, -1699 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1699\right)±\sqrt{\left(-1699\right)^{2}}}{2\times 10}$$

Tuhia te pūtakerua o te \left(-1699\right)^{2}.

$$x=\frac{-\left(-1699\right)±1699}{2\times 10}$$

Ko te tauaro o -1699 ko 1699.

$$x=\frac{1699±1699}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{1699±1699}{20}$$

Nā, me whakaoti te whārite x=\frac{1699±1699}{20} ina he tāpiri te ±. Tāpiri 1699 ki te 1699.

$$x=\frac{3398}{20}$$

Whakahekea te hautanga \frac{3398}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1699}{10}$$

Nā, me whakaoti te whārite x=\frac{1699±1699}{20} ina he tango te ±. Tango 1699 mai i 1699.

$$x=\frac{0}{20}$$

Whakawehe 0 ki te 20.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{1699}{10} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 10 ki te 150-x.

$$x=x\left(200+1500-10x\right)$$

Tāpirihia te 200 ki te 1500, ka 1700.

$$x=x\left(1700-10x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 1700-10x.

$$x=1700x-10x^{2}$$

Tangohia te 1700x mai i ngā taha e rua.

$$x-1700x=-10x^{2}$$

Pahekotia te x me -1700x, ka -1699x.

$$-1699x=-10x^{2}$$

Me tāpiri te 10x^{2} ki ngā taha e rua.

$$-1699x+10x^{2}=0$$

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.

$$10x^{2}-1699x=0$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10x^{2}-1699x}{10}=\frac{0}{10}$$

Mā te whakawehe ki te 10 ka wetekia te whakareanga ki te 10.

$$x^{2}-\frac{1699}{10}x=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$x^{2}-\frac{1699}{10}x=0$$

Whakawehea te -\frac{1699}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1699}{20}. Nā, tāpiria te pūrua o te -\frac{1699}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1699}{10}x+\left(-\frac{1699}{20}\right)^{2}=\left(-\frac{1699}{20}\right)^{2}$$

Pūruatia -\frac{1699}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1699}{10}x+\frac{2886601}{400}=\frac{2886601}{400}$$

Tauwehea x^{2}-\frac{1699}{10}x+\frac{2886601}{400}. 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}.

$$\left(x-\frac{1699}{20}\right)^{2}=\frac{2886601}{400}$$

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

$$\sqrt{\left(x-\frac{1699}{20}\right)^{2}}=\sqrt{\frac{2886601}{400}}$$

Whakarūnātia.

$$x-\frac{1699}{20}=\frac{1699}{20} x-\frac{1699}{20}=-\frac{1699}{20}$$

Me tāpiri \frac{1699}{20} ki ngā taha e rua o te whārite.

$$x=\frac{1699}{10} x=0$$