Whakaoti i te x^2+120^2=(5+x)^2

$$x ^ { 2 } + 120 ^ { 2 } = ( 5 + x ) ^ { 2 }$$

Whakaoti mō x

$$x = \frac{2875}{2} = 1437\frac{1}{2} = 1437.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 120 mā te pū o 2, kia riro ko 14400.

$$x^{2}+14400=\left(5+x\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(5+x\right)^{2}.

$$x^{2}+14400=25+10x+x^{2}$$

Tangohia te 10x mai i ngā taha e rua.

$$x^{2}+14400-10x=25+x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x^{2}+14400-10x-x^{2}=25$$

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

$$14400-10x=25$$

Tangohia te 14400 mai i ngā taha e rua.

$$-10x=25-14400$$

Tangohia te 14400 i te 25, ka -14375.

$$-10x=-14375$$

Whakawehea ngā taha e rua ki te -10.

$$x=\frac{-14375}{-10}$$

Whakahekea te hautanga \frac{-14375}{-10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -5.

$$x=\frac{2875}{2}$$