Solve -sqrt{b}=4-sqrt{a}

$$- \sqrt { b } = 4 - \sqrt { a }$$

Solve for a

$$a=\left(\sqrt{b}+4\right)^{2}$$

$$b\geq 0$$

Steps for Solving Radical Equations

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

$$4-\sqrt{a}=-\sqrt{b}$$

Subtract 4 from both sides.

$$-\sqrt{a}=-\sqrt{b}-4$$

Divide both sides by -1.

$$\frac{-\sqrt{a}}{-1}=\frac{-\sqrt{b}-4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{a}=\frac{-\sqrt{b}-4}{-1}$$

Divide -\sqrt{b}-4 by -1.

$$\sqrt{a}=\sqrt{b}+4$$

Square both sides of the equation.

$$a=\left(\sqrt{b}+4\right)^{2}$$

Solve for b

$$b=\left(-\sqrt{a}+4\right)^{2}$$

$$a\geq 0\text{ and }-\left(-\sqrt{a}+4\right)\geq 0$$

Steps for Solving Radical Equations

Divide both sides by -1.

$$\frac{-\sqrt{b}}{-1}=\frac{-\sqrt{a}+4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{b}=\frac{-\sqrt{a}+4}{-1}$$

Divide 4-\sqrt{a} by -1.

$$\sqrt{b}=\sqrt{a}-4$$

Square both sides of the equation.

$$b=\left(\sqrt{a}-4\right)^{2}$$

Solve for a (complex solution)

$$a=\left(\sqrt{b}+4\right)^{2}$$

$$arg(\sqrt{b}+4)<\pi$$

Solve for b (complex solution)

$$b=\left(-\sqrt{a}+4\right)^{2}$$

$$a=16\text{ or }arg(-\sqrt{a}+4)\geq \pi$$