Solve sqrt{2u+3}=sqrt{-2u-1}

$$\sqrt { 2 u + 3 } = \sqrt { - 2 u - 1 }$$

Solve for u

$$u=-1$$

Solution Steps

Square both sides of the equation.

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

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

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

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

$$2u+3=-2u-1$$

Add 2u to both sides.

$$2u+3+2u=-1$$

Combine 2u and 2u to get 4u.

$$4u+3=-1$$

Subtract 3 from both sides.

$$4u=-1-3$$

Subtract 3 from -1 to get -4.

$$4u=-4$$

Divide both sides by 4.

$$u=\frac{-4}{4}$$

Divide -4 by 4 to get -1.

$$u=-1$$

Substitute -1 for u in the equation \sqrt{2u+3}=\sqrt{-2u-1}.

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

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

$$1=1$$

Equation \sqrt{2u+3}=\sqrt{-2u-1} has a unique solution.

$$u=-1$$