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

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

Resolver L

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

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(2x-3\right)^{2}.

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

Usa a propiedade distributiva para multiplicar -5 por 2x-3.

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

Usa a propiedade distributiva para multiplicar -10x+15 por x+1 e combina os termos semellantes.

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

Combina 4x^{2} e -10x^{2} para obter -6x^{2}.

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

Combina -12x e 5x para obter -7x.

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

Suma 9 e 15 para obter 24.

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

Resolver x (complex solution)

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

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

Resolver x

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

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