Whakaoti i te x^2+40x/x^2+3x-2=0

$$\frac { x ^ { 2 } + 40 x } { x ^ { 2 } + 3 x - 2 } = 0$$

Whakaoti mō x

$$x=-40$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia ngā taha e rua o te whārite ki te \left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right).

$$x^{2}+40x=0$$

Tauwehea te x.

$$x\left(x+40\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x+40=0.

$$x=0 x=-40$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te \left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right).

$$x^{2}+40x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 40 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-40±\sqrt{40^{2}}}{2}$$

Tuhia te pūtakerua o te 40^{2}.

$$x=\frac{-40±40}{2}$$

Nā, me whakaoti te whārite x=\frac{-40±40}{2} ina he tāpiri te ±. Tāpiri -40 ki te 40.

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

Whakawehe 0 ki te 2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-40±40}{2} ina he tango te ±. Tango 40 mai i -40.

$$x=-\frac{80}{2}$$

Whakawehe -80 ki te 2.

$$x=-40$$

Kua oti te whārite te whakatau.

$$x=0 x=-40$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te \left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right).

$$x^{2}+40x=0$$

Whakawehea te 40, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 20. Nā, tāpiria te pūrua o te 20 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+40x+20^{2}=20^{2}$$

Pūrua 20.

$$x^{2}+40x+400=400$$

Tauwehea x^{2}+40x+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}.

$$\left(x+20\right)^{2}=400$$

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

$$\sqrt{\left(x+20\right)^{2}}=\sqrt{400}$$

Whakarūnātia.

$$x+20=20 x+20=-20$$

Me tango 20 mai i ngā taha e rua o te whārite.

$$x=0 x=-40$$