Whakaoti i te 18-x+(sqrt{x^2+144})=42

$$18-x+( \sqrt{ { x }^{ 2 } +144 } )=42$$

Whakaoti mō x

$$x=-9$$

Ngā Upane Otinga

Me tango 18-x mai i ngā taha e rua o te whārite.

$$\sqrt{x^{2}+144}=42-\left(18-x\right)$$

Hei kimi i te tauaro o 18-x, kimihia te tauaro o ia taurangi.

$$\sqrt{x^{2}+144}=42-18+x$$

Tangohia te 18 i te 42, ka 24.

$$\sqrt{x^{2}+144}=24+x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x^{2}+144}\right)^{2}=\left(24+x\right)^{2}$$

Tātaihia te \sqrt{x^{2}+144} mā te pū o 2, kia riro ko x^{2}+144.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(24+x\right)^{2}.

$$x^{2}+144=576+48x+x^{2}$$

Tangohia te 48x mai i ngā taha e rua.

$$x^{2}+144-48x=576+x^{2}$$

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

$$x^{2}+144-48x-x^{2}=576$$

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

$$144-48x=576$$

Tangohia te 144 mai i ngā taha e rua.

$$-48x=576-144$$

Tangohia te 144 i te 576, ka 432.

$$-48x=432$$

Whakawehea ngā taha e rua ki te -48.

$$x=\frac{432}{-48}$$

Whakawehea te 432 ki te -48, kia riro ko -9.

$$x=-9$$

Whakakapia te -9 mō te x i te whārite 18-x+\sqrt{x^{2}+144}=42.

$$18-\left(-9\right)+\sqrt{\left(-9\right)^{2}+144}=42$$

Whakarūnātia. Ko te uara x=-9 kua ngata te whārite.

$$42=42$$

Ko te whārite \sqrt{x^{2}+144}=x+24 he rongoā ahurei.

$$x=-9$$