Whakaoti i te 0.09(x+30)=[0.3(x+30)]^2/x+50

$$0.09 ( x + 30 ) = \frac { [ 0.3 ( x + 30 ) ] ^ { 2 } } { x + 50 }$$

Whakaoti mō x

$$x=-30$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki -50 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+50.

$$0.09\left(x+30\right)\left(x+50\right)=\left(0.3\left(x+30\right)\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 0.09 ki te x+30.

$$\left(0.09x+2.7\right)\left(x+50\right)=\left(0.3\left(x+30\right)\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 0.09x+2.7 ki te x+50 ka whakakotahi i ngā kupu rite.

$$0.09x^{2}+7.2x+135=\left(0.3\left(x+30\right)\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 0.3 ki te x+30.

$$0.09x^{2}+7.2x+135=\left(0.3x+9\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(0.3x+9\right)^{2}.

$$0.09x^{2}+7.2x+135=0.09x^{2}+5.4x+81$$

Tangohia te 0.09x^{2} mai i ngā taha e rua.

$$0.09x^{2}+7.2x+135-0.09x^{2}=5.4x+81$$

Pahekotia te 0.09x^{2} me -0.09x^{2}, ka 0.

$$7.2x+135=5.4x+81$$

Tangohia te 5.4x mai i ngā taha e rua.

$$7.2x+135-5.4x=81$$

Pahekotia te 7.2x me -5.4x, ka 1.8x.

$$1.8x+135=81$$

Tangohia te 135 mai i ngā taha e rua.

$$1.8x=81-135$$

Tangohia te 135 i te 81, ka -54.

$$1.8x=-54$$

Whakawehea ngā taha e rua ki te 1.8.

$$x=\frac{-54}{1.8}$$

Whakarohaina te \frac{-54}{1.8} mā te whakarea i te taurunga me te tauraro ki te 10.

$$x=\frac{-540}{18}$$

Whakawehea te -540 ki te 18, kia riro ko -30.

$$x=-30$$