Solve x=sqrt{4-x^2}

$$x = \sqrt { 4 - x ^ { 2 } }$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

Solution Steps

Square both sides of the equation.

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

Calculate \sqrt{4-x^{2}} to the power of 2 and get 4-x^{2}.

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

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}=4$$

Divide both sides by 2.

$$x^{2}=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

$$x=\sqrt{2} x=-\sqrt{2}$$

Substitute \sqrt{2} for x in the equation x=\sqrt{4-x^{2}}.

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

Simplify. The value x=\sqrt{2} satisfies the equation.

$$2^{\frac{1}{2}}=2^{\frac{1}{2}}$$

Substitute -\sqrt{2} for x in the equation x=\sqrt{4-x^{2}}.

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

Simplify. The value x=-\sqrt{2} does not satisfy the equation because the left and the right hand side have opposite signs.

$$-2^{\frac{1}{2}}=2^{\frac{1}{2}}$$

Equation x=\sqrt{4-x^{2}} has a unique solution.

$$x=\sqrt{2}$$