Whakaoti i te frac{4pmsqrt{-4^2-4*(-3)*39}}{2*(-3)}=frac{4pmsqrt{-16+468}}{-6}

$$\frac { 4 \pm \sqrt { - 4 ^ { 2 } - 4 \cdot ( - 3 ) \cdot 39 } } { 2 \cdot ( - 3 ) } = \frac { 4 \pm \sqrt { - 16 + 468 } } { - 6 }$$

Manatoko

Ngā Upane Otinga

Whakareatia ngā taha e rua o te whārite ki te -6.

$$4±\sqrt{-4^{2}-4\left(-3\right)\times 39}=4±\sqrt{-16+468}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$4±\sqrt{-16-4\left(-3\right)\times 39}=4±\sqrt{-16+468}$$

Whakareatia te 4 ki te -3, ka -12.

$$4±\sqrt{-16-\left(-12\times 39\right)}=4±\sqrt{-16+468}$$

Whakareatia te -12 ki te 39, ka -468.

$$4±\sqrt{-16-\left(-468\right)}=4±\sqrt{-16+468}$$

Ko te tauaro o -468 ko 468.

$$4±\sqrt{-16+468}=4±\sqrt{-16+468}$$

Tāpirihia te -16 ki te 468, ka 452.

$$4±\sqrt{452}=4±\sqrt{-16+468}$$

Tauwehea te 452=2^{2}\times 113. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 113} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{113}. Tuhia te pūtakerua o te 2^{2}.

$$4±2\sqrt{113}=4±\sqrt{-16+468}$$

Tāpirihia te -16 ki te 468, ka 452.

$$4±2\sqrt{113}=4±\sqrt{452}$$

Tauwehea te 452=2^{2}\times 113. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 113} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{113}. Tuhia te pūtakerua o te 2^{2}.

$$4±2\sqrt{113}=4±2\sqrt{113}$$

Tangohia te 4±2\sqrt{113} mai i ngā taha e rua.

$$4±2\sqrt{113}-\left(4±2\sqrt{113}\right)=0$$

Pahekotia te 4±2\sqrt{113} me -\left(4±2\sqrt{113}\right), ka 0.

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$