Solve sqrt{x+3}=sqrt{1-x}

$$\sqrt { x + 3 } = \sqrt { 1 - x }$$

Solve for x

$$x=-1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x+3}\right)^{2}=\left(\sqrt{1-x}\right)^{2}$$

Calculate \sqrt{x+3} to the power of 2 and get x+3.

$$x+3=\left(\sqrt{1-x}\right)^{2}$$

Calculate \sqrt{1-x} to the power of 2 and get 1-x.

$$x+3=1-x$$

Add x to both sides.

$$x+3+x=1$$

Combine x and x to get 2x.

$$2x+3=1$$

Subtract 3 from both sides.

$$2x=1-3$$

Subtract 3 from 1 to get -2.

$$2x=-2$$

Divide both sides by 2.

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

Divide -2 by 2 to get -1.

$$x=-1$$

Substitute -1 for x in the equation \sqrt{x+3}=\sqrt{1-x}.

$$\sqrt{-1+3}=\sqrt{1-\left(-1\right)}$$

Simplify. The value x=-1 satisfies the equation.

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

Equation \sqrt{x+3}=\sqrt{1-x} has a unique solution.

$$x=-1$$