Whakaoti i te 49x^2+2x-15

$$49 { x }^{ 2 } +2x-15$$

Tauwehe

$$49\left(x-\frac{-4\sqrt{46}-1}{49}\right)\left(x-\frac{4\sqrt{46}-1}{49}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$49x^{2}+2x-15=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 49\left(-15\right)}}{2\times 49}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 49\left(-15\right)}}{2\times 49}$$

Whakareatia -4 ki te 49.

$$x=\frac{-2±\sqrt{4-196\left(-15\right)}}{2\times 49}$$

Whakareatia -196 ki te -15.

$$x=\frac{-2±\sqrt{4+2940}}{2\times 49}$$

Tāpiri 4 ki te 2940.

$$x=\frac{-2±\sqrt{2944}}{2\times 49}$$

Tuhia te pūtakerua o te 2944.

$$x=\frac{-2±8\sqrt{46}}{2\times 49}$$

Whakareatia 2 ki te 49.

$$x=\frac{-2±8\sqrt{46}}{98}$$

Nā, me whakaoti te whārite x=\frac{-2±8\sqrt{46}}{98} ina he tāpiri te ±. Tāpiri -2 ki te 8\sqrt{46}.

$$x=\frac{8\sqrt{46}-2}{98}$$

Whakawehe -2+8\sqrt{46} ki te 98.

$$x=\frac{4\sqrt{46}-1}{49}$$

Nā, me whakaoti te whārite x=\frac{-2±8\sqrt{46}}{98} ina he tango te ±. Tango 8\sqrt{46} mai i -2.

$$x=\frac{-8\sqrt{46}-2}{98}$$

Whakawehe -2-8\sqrt{46} ki te 98.

$$x=\frac{-4\sqrt{46}-1}{49}$$

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{-1+4\sqrt{46}}{49} mō te x_{1} me te \frac{-1-4\sqrt{46}}{49} mō te x_{2}.

$$49x^{2}+2x-15=49\left(x-\frac{4\sqrt{46}-1}{49}\right)\left(x-\frac{-4\sqrt{46}-1}{49}\right)$$

Aromātai

$$49x^{2}+2x-15$$