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

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

Solve for A

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

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

Divide each term of 4x^{2}-12x+9 by 44 to get \frac{1}{11}x^{2}-\frac{3}{11}x+\frac{9}{44}.

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

To find the opposite of \frac{1}{11}x^{2}-\frac{3}{11}x+\frac{9}{44}, find the opposite of each term.

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

Subtract \frac{9}{44} from 36 to get \frac{1575}{44}.

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

Solve for x (complex solution)

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

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

Solve for x

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

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