Atrisiniet A=36-(2x-3)^2:44

$$A = 36 - ( 2 x - 3 ) ^ { 2 } : 44$$

Atrast A

$$A=-\frac{\left(2x-3\right)^{2}}{44}+36$$

Atrisinājuma darbības

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(2x-3\right)^{2}.

$$A=36-\frac{4x^{2}-12x+9}{44}$$

Daliet katru 4x^{2}-12x+9 locekli ar 44, lai iegūtu \frac{1}{11}x^{2}-\frac{3}{11}x+\frac{9}{44}.

$$A=36-\left(\frac{1}{11}x^{2}-\frac{3}{11}x+\frac{9}{44}\right)$$

Lai atrastu \frac{1}{11}x^{2}-\frac{3}{11}x+\frac{9}{44} pretējo vērtību, atrodiet katra locekļa pretējo vērtību.

$$A=36-\frac{1}{11}x^{2}+\frac{3}{11}x-\frac{9}{44}$$

Atņemiet \frac{9}{44} no 36, lai iegūtu \frac{1575}{44}.

$$A=\frac{1575}{44}-\frac{1}{11}x^{2}+\frac{3}{11}x$$

Atrast x (complex solution)

$$x=-\sqrt{396-11A}+\frac{3}{2}$$

$$x=\sqrt{396-11A}+\frac{3}{2}$$

Atrast x

$$x=-\sqrt{396-11A}+\frac{3}{2}$$

$$x=\sqrt{396-11A}+\frac{3}{2}\text{, }A\leq 36$$