Whakaoti i te 32x^2-56x+20x-35+15x^2-40

$$32 x ^ { 2 } - 56 x + 20 x - 35 + 15 x ^ { 2 } - 40$$

Aromātai

$$47x^{2}-36x-75$$

Ngā Upane Otinga

Pahekotia te -56x me 20x, ka -36x.

$$32x^{2}-36x-35+15x^{2}-40$$

Pahekotia te 32x^{2} me 15x^{2}, ka 47x^{2}.

$$47x^{2}-36x-35-40$$

Tangohia te 40 i te -35, ka -75.

$$47x^{2}-36x-75$$

Tauwehe

$$47\left(x-\frac{18-\sqrt{3849}}{47}\right)\left(x-\frac{\sqrt{3849}+18}{47}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -56x me 20x, ka -36x.

$$factor(32x^{2}-36x-35+15x^{2}-40)$$

Pahekotia te 32x^{2} me 15x^{2}, ka 47x^{2}.

$$factor(47x^{2}-36x-35-40)$$

Tangohia te 40 i te -35, ka -75.

$$factor(47x^{2}-36x-75)$$

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$47x^{2}-36x-75=0$$

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.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 47\left(-75\right)}}{2\times 47}$$

Pūrua -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 47\left(-75\right)}}{2\times 47}$$

Whakareatia -4 ki te 47.

$$x=\frac{-\left(-36\right)±\sqrt{1296-188\left(-75\right)}}{2\times 47}$$

Whakareatia -188 ki te -75.

$$x=\frac{-\left(-36\right)±\sqrt{1296+14100}}{2\times 47}$$

Tāpiri 1296 ki te 14100.

$$x=\frac{-\left(-36\right)±\sqrt{15396}}{2\times 47}$$

Tuhia te pūtakerua o te 15396.

$$x=\frac{-\left(-36\right)±2\sqrt{3849}}{2\times 47}$$

Ko te tauaro o -36 ko 36.

$$x=\frac{36±2\sqrt{3849}}{2\times 47}$$

Whakareatia 2 ki te 47.

$$x=\frac{36±2\sqrt{3849}}{94}$$

Nā, me whakaoti te whārite x=\frac{36±2\sqrt{3849}}{94} ina he tāpiri te ±. Tāpiri 36 ki te 2\sqrt{3849}.

$$x=\frac{2\sqrt{3849}+36}{94}$$

Whakawehe 36+2\sqrt{3849} ki te 94.

$$x=\frac{\sqrt{3849}+18}{47}$$

Nā, me whakaoti te whārite x=\frac{36±2\sqrt{3849}}{94} ina he tango te ±. Tango 2\sqrt{3849} mai i 36.

$$x=\frac{36-2\sqrt{3849}}{94}$$

Whakawehe 36-2\sqrt{3849} ki te 94.

$$x=\frac{18-\sqrt{3849}}{47}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{18+\sqrt{3849}}{47} mō te x_{1} me te \frac{18-\sqrt{3849}}{47} mō te x_{2}.

$$47x^{2}-36x-75=47\left(x-\frac{\sqrt{3849}+18}{47}\right)\left(x-\frac{18-\sqrt{3849}}{47}\right)$$