Whakaoti i te lambda^2+75x-1900=0

$$\lambda ^ { 2 } + 75 x - 1900 = 0$$

Whakaoti mō x

$$x=-\frac{\lambda ^{2}}{75}+\frac{76}{3}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \lambda ^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$75x-1900=-\lambda ^{2}$$

Me tāpiri te 1900 ki ngā taha e rua.

$$75x=-\lambda ^{2}+1900$$

He hanga arowhānui tō te whārite.

$$75x=1900-\lambda ^{2}$$

Whakawehea ngā taha e rua ki te 75.

$$\frac{75x}{75}=\frac{1900-\lambda ^{2}}{75}$$

Mā te whakawehe ki te 75 ka wetekia te whakareanga ki te 75.

$$x=\frac{1900-\lambda ^{2}}{75}$$

Whakawehe -\lambda ^{2}+1900 ki te 75.

$$x=-\frac{\lambda ^{2}}{75}+\frac{76}{3}$$

Whakaoti mō λ (complex solution)

$$\lambda =-5\sqrt{76-3x}$$

$$\lambda =5\sqrt{76-3x}$$

Whakaoti mō λ

$$\lambda =5\sqrt{76-3x}$$

$$\lambda =-5\sqrt{76-3x}\text{, }x\leq \frac{76}{3}$$