Whakaoti i te 80=x+sqrt{36+x^2}

$$80 = x + \sqrt { 36 + x ^ { 2 } }$$

Whakaoti mō x

$$x = \frac{1591}{40} = 39\frac{31}{40} = 39.775$$

Ngā Upane Otinga

Me tango x mai i ngā taha e rua o te whārite.

$$80-x=\sqrt{36+x^{2}}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(80-x\right)^{2}=\left(\sqrt{36+x^{2}}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(80-x\right)^{2}.

$$6400-160x+x^{2}=\left(\sqrt{36+x^{2}}\right)^{2}$$

Tātaihia te \sqrt{36+x^{2}} mā te pū o 2, kia riro ko 36+x^{2}.

$$6400-160x+x^{2}=36+x^{2}$$

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

$$6400-160x+x^{2}-x^{2}=36$$

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

$$6400-160x=36$$

Tangohia te 6400 mai i ngā taha e rua.

$$-160x=36-6400$$

Tangohia te 6400 i te 36, ka -6364.

$$-160x=-6364$$

Whakawehea ngā taha e rua ki te -160.

$$x=\frac{-6364}{-160}$$

Whakahekea te hautanga \frac{-6364}{-160} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -4.

$$x=\frac{1591}{40}$$

Whakakapia te \frac{1591}{40} mō te x i te whārite 80=x+\sqrt{36+x^{2}}.

$$80=\frac{1591}{40}+\sqrt{36+\left(\frac{1591}{40}\right)^{2}}$$

Whakarūnātia. Ko te uara x=\frac{1591}{40} kua ngata te whārite.

$$80=80$$

Ko te whārite 80-x=\sqrt{x^{2}+36} he rongoā ahurei.

$$x=\frac{1591}{40}$$