Whakaoti i te 7^{2}+3x=(24^4:12^4*2^-2:2*2^0)x

$$7 ^ { 2 } + 3 x = ( 24 ^ { 4 } : 12 ^ { 4 } \cdot 2 ^ { - 2 } : 2 \cdot 2 ^ { 0 } ) x$$

Whakaoti mō x

$$x=-49$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2\times 7^{2}+6x=\frac{24^{4}}{12^{4}}\times 2^{-2}\times 2^{0}x$$

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$2\times 49+6x=\frac{24^{4}}{12^{4}}\times 2^{-2}\times 2^{0}x$$

Whakareatia te 2 ki te 49, ka 98.

$$98+6x=\frac{24^{4}}{12^{4}}\times 2^{-2}\times 2^{0}x$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -2 me te 0 kia riro ai te -2.

$$98+6x=\frac{24^{4}}{12^{4}}\times 2^{-2}x$$

Tātaihia te 24 mā te pū o 4, kia riro ko 331776.

$$98+6x=\frac{331776}{12^{4}}\times 2^{-2}x$$

Tātaihia te 12 mā te pū o 4, kia riro ko 20736.

$$98+6x=\frac{331776}{20736}\times 2^{-2}x$$

Whakawehea te 331776 ki te 20736, kia riro ko 16.

$$98+6x=16\times 2^{-2}x$$

Tātaihia te 2 mā te pū o -2, kia riro ko \frac{1}{4}.

$$98+6x=16\times \frac{1}{4}x$$

Whakareatia te 16 ki te \frac{1}{4}, ka 4.

$$98+6x=4x$$

Tangohia te 4x mai i ngā taha e rua.

$$98+6x-4x=0$$

Pahekotia te 6x me -4x, ka 2x.

$$98+2x=0$$

Tangohia te 98 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2x=-98$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{-98}{2}$$

Whakawehea te -98 ki te 2, kia riro ko -49.

$$x=-49$$