Whakaoti i te 26x=x^2+16x

$$26 x = x ^ { 2 } + 16 x$$

Whakaoti mō x

$$x=10$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$26x-x^{2}=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$26x-x^{2}-16x=0$$

Pahekotia te 26x me -16x, ka 10x.

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

Tauwehea te x.

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

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

$$x=0 x=10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$26x-x^{2}=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$26x-x^{2}-16x=0$$

Pahekotia te 26x me -16x, ka 10x.

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

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.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 10 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 10^{2}.

$$x=\frac{-10±10}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-10±10}{-2}$$

Nā, me whakaoti te whārite x=\frac{-10±10}{-2} ina he tāpiri te ±. Tāpiri -10 ki te 10.

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

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-10±10}{-2} ina he tango te ±. Tango 10 mai i -10.

$$x=-\frac{20}{-2}$$

Whakawehe -20 ki te -2.

$$x=10$$

Kua oti te whārite te whakatau.

$$x=0 x=10$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$26x-x^{2}=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$26x-x^{2}-16x=0$$

Pahekotia te 26x me -16x, ka 10x.

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

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.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+10x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{10}{-1}x=\frac{0}{-1}$$

Whakawehe 10 ki te -1.

$$x^{2}-10x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

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

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.

$$x=10 x=0$$