Whakaoti i te 10^2-x^2=8^2-left(12-xright)^2

$${ 10 }^{ 2 } - { x }^{ 2 } = { 8 }^{ 2 } - { \left(12-x \right) }^{ 2 }$$

Whakaoti mō x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$100-x^{2}=8^{2}-\left(12-x\right)^{2}$$

Tātaihia te 8 mā te pū o 2, kia riro ko 64.

$$100-x^{2}=64-\left(12-x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(12-x\right)^{2}.

$$100-x^{2}=64-\left(144-24x+x^{2}\right)$$

Hei kimi i te tauaro o 144-24x+x^{2}, kimihia te tauaro o ia taurangi.

$$100-x^{2}=64-144+24x-x^{2}$$

Tangohia te 144 i te 64, ka -80.

$$100-x^{2}=-80+24x-x^{2}$$

Tangohia te 24x mai i ngā taha e rua.

$$100-x^{2}-24x=-80-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$100-x^{2}-24x+x^{2}=-80$$

Pahekotia te -x^{2} me x^{2}, ka 0.

$$100-24x=-80$$

Tangohia te 100 mai i ngā taha e rua.

$$-24x=-80-100$$

Tangohia te 100 i te -80, ka -180.

$$-24x=-180$$

Whakawehea ngā taha e rua ki te -24.

$$x=\frac{-180}{-24}$$

Whakahekea te hautanga \frac{-180}{-24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -12.

$$x=\frac{15}{2}$$