Solve sqrt{-4w-2}=sqrt{w+3}

$$\sqrt { - 4 w - 2 } = \sqrt { w + 3 }$$

Solve for w

$$w=-1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{-4w-2}\right)^{2}=\left(\sqrt{w+3}\right)^{2}$$

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

$$-4w-2=\left(\sqrt{w+3}\right)^{2}$$

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

$$-4w-2=w+3$$

Subtract w from both sides.

$$-4w-2-w=3$$

Combine -4w and -w to get -5w.

$$-5w-2=3$$

Add 2 to both sides.

$$-5w=3+2$$

Add 3 and 2 to get 5.

$$-5w=5$$

Divide both sides by -5.

$$w=\frac{5}{-5}$$

Divide 5 by -5 to get -1.

$$w=-1$$

Substitute -1 for w in the equation \sqrt{-4w-2}=\sqrt{w+3}.

$$\sqrt{-4\left(-1\right)-2}=\sqrt{-1+3}$$

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

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

Equation \sqrt{-4w-2}=\sqrt{w+3} has a unique solution.

$$w=-1$$