Issolvi L=left(2x-3right)^2-5left(2x-3right)left(x+1right)

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

Solvi għal L

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2x-3\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika -5 b'2x-3.

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

Uża l-propjetà distributtiva biex timmultiplika -10x+15 b'x+1 u kkombina termini simili.

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

Ikkombina 4x^{2} u -10x^{2} biex tikseb -6x^{2}.

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

Ikkombina -12x u 5x biex tikseb -7x.

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

Żid 9 u 15 biex tikseb 24.

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

Solvi għal x (complex solution)

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

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

Solvi għal x

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

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