Whakaoti i te L=left(2x-3right)^2-5left(2x-3right)left(x+1right)

$$L = { \left(2x-3 \right) }^{ 2 } -5 \left( 2x-3 \right) \left( x+1 \right)$$

Whakaoti mō L

$$L=24-7x-6x^{2}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-3\right)^{2}.

$$L=4x^{2}-12x+9-5\left(2x-3\right)\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te 2x-3.

$$L=4x^{2}-12x+9+\left(-10x+15\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -10x+15 ki te x+1 ka whakakotahi i ngā kupu rite.

$$L=4x^{2}-12x+9-10x^{2}+5x+15$$

Pahekotia te 4x^{2} me -10x^{2}, ka -6x^{2}.

$$L=-6x^{2}-12x+9+5x+15$$

Pahekotia te -12x me 5x, ka -7x.

$$L=-6x^{2}-7x+9+15$$

Tāpirihia te 9 ki te 15, ka 24.

$$L=-6x^{2}-7x+24$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{625-24L}-7}{12}$$

$$x=\frac{-\sqrt{625-24L}-7}{12}$$

Whakaoti mō x

$$x=\frac{\sqrt{625-24L}-7}{12}$$

$$x=\frac{-\sqrt{625-24L}-7}{12}\text{, }L\leq \frac{625}{24}$$