Solve x*2^x-2^x-2ax-1=0

$$x \cdot 2 ^ { x } - 2 ^ { x } - 2 a x - 1 = 0$$

Solve for a

$$a=\frac{x\times 2^{x}-2^{x}-1}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract x\times 2^{x}-2^{x} from both sides. Anything subtracted from zero gives its negation.

$$-2ax-1=-\left(x\times 2^{x}-2^{x}\right)$$

Add 1 to both sides.

$$-2ax=-\left(x\times 2^{x}-2^{x}\right)+1$$

To find the opposite of x\times 2^{x}-2^{x}, find the opposite of each term.

$$-2ax=-x\times 2^{x}+2^{x}+1$$

The equation is in standard form.

$$\left(-2x\right)a=1+2^{x}-x\times 2^{x}$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)a}{-2x}=\frac{1+2^{x}-x\times 2^{x}}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$a=\frac{1+2^{x}-x\times 2^{x}}{-2x}$$

Divide -x\times 2^{x}+2^{x}+1 by -2x.

$$a=-\frac{1+2^{x}-x\times 2^{x}}{2x}$$