Solve 2a=sqrt{12^2+x}

$$2a = \sqrt{ { 12 }^{ 2 } +x }$$

Solve for a (complex solution)

$$a=\frac{\sqrt{x+144}}{2}$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$2a=\sqrt{144+x}$$

The equation is in standard form.

$$2a=\sqrt{x+144}$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{\sqrt{x+144}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{\sqrt{x+144}}{2}$$

Solve for a

$$a=\frac{\sqrt{x+144}}{2}$$

$$x\geq -144$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$2a=\sqrt{144+x}$$

The equation is in standard form.

$$2a=\sqrt{x+144}$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{\sqrt{x+144}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{\sqrt{x+144}}{2}$$

Solve for x

$$x=4\left(a^{2}-36\right)$$

$$a\geq 0$$

Steps for Solving Radical Equations

Calculate 12 to the power of 2 and get 144.

$$2a=\sqrt{144+x}$$

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

$$\sqrt{144+x}=2a$$

Square both sides of the equation.

$$x+144=4a^{2}$$

Subtract 144 from both sides of the equation.

$$x+144-144=4a^{2}-144$$

Subtracting 144 from itself leaves 0.

$$x=4a^{2}-144$$

Solve for x (complex solution)

$$x=4\left(a^{2}-36\right)$$

$$arg(a)<\pi \text{ or }a=0$$