Solve a-sqrt{a^2-8^2}=16x-64

$$a - \sqrt { a ^ { 2 } - 8 ^ { 2 } } = 16 x - 64$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{a^{2}-64}+a+64}{16}$$

Steps for Solving Linear Equation

Calculate 8 to the power of 2 and get 64.

$$a-\sqrt{a^{2}-64}=16x-64$$

Swap sides so that all variable terms are on the left hand side.

$$16x-64=a-\sqrt{a^{2}-64}$$

Add 64 to both sides.

$$16x=a-\sqrt{a^{2}-64}+64$$

The equation is in standard form.

$$16x=-\sqrt{a^{2}-64}+a+64$$

Divide both sides by 16.

$$\frac{16x}{16}=\frac{-\sqrt{a^{2}-64}+a+64}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x=\frac{-\sqrt{a^{2}-64}+a+64}{16}$$

Divide a-\sqrt{a^{2}-64}+64 by 16.

$$x=-\frac{\sqrt{a^{2}-64}}{16}+\frac{a}{16}+4$$

Solve for x

$$x=\frac{-\sqrt{a^{2}-64}+a+64}{16}$$

$$|a|\geq 8$$

Steps for Solving Linear Equation

Calculate 8 to the power of 2 and get 64.

$$a-\sqrt{a^{2}-64}=16x-64$$

Swap sides so that all variable terms are on the left hand side.

$$16x-64=a-\sqrt{a^{2}-64}$$

Add 64 to both sides.

$$16x=a-\sqrt{a^{2}-64}+64$$

The equation is in standard form.

$$16x=-\sqrt{a^{2}-64}+a+64$$

Divide both sides by 16.

$$\frac{16x}{16}=\frac{-\sqrt{a^{2}-64}+a+64}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x=\frac{-\sqrt{a^{2}-64}+a+64}{16}$$

Divide a-\sqrt{a^{2}-64}+64 by 16.

$$x=-\frac{\sqrt{a^{2}-64}}{16}+\frac{a}{16}+4$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{2\left(-4x^{2}+32x-65\right)}{x-4}\text{, }&x\neq 4\text{ and }arg(\frac{8x^{2}-64x+130}{x-4}-16x+64)<\pi \\a=16\left(x-4\right)\text{, }&x=\frac{9}{2}\text{ or }x=\frac{7}{2}\end{matrix}\right.$$

Solve for a

$$a=-\frac{2\left(-4x^{2}+32x-65\right)}{x-4}$$

$$x\leq \frac{7}{2}\text{ or }\left(x>4\text{ and }x\leq \frac{9}{2}\right)$$