To solve for , first divide by two.

The two in the denominator cancels the two in the numerator.

From here, square both sides of the equation. Squaring a square root cancels it out.

To check for extraneous solutions, simply substitute into the original equation the value found for .

To solve for , add three to both sides of the equation.

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From here, take the square root of both sides. Taking the square root of a squared term eliminates the square.

Next, check for extraneous solutions. Substitute each potential solution into the original equation to verify if it results in a legal solution.

Substituting in positive four.

Substituting in negative four.

Therefore, both answers are verified solutions.

To solve for , combine the like terms on the right-hand side.

From here, square both sides of the equation. Squaring a square root sign cancels it.

Now, subtract two from both sides so that all constants are on one side and all variables are on the other side.

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Next, divide both sides by negative one.

Lastly, check for extraneous solutions by substituting in the value found to  into the original equation.

Therefore, the solution is verified.

To solve for , first combine the like terms on the right-hand side of the equation.

Next, subtract two from both sides.

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Now, divide both sides by negative one.

From here, square both sides.

Next, subtract one from both side to solve .

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Lastly, check for extraneous solutions.

Since one of the values is a correct solution this verifies  as a solution.

The first step is to square each side of the inequality.

Now simplify each side.

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

Now we can use the quadratic formula.

Recall the quadratic formula.

Where , , and , correspond to coefficients in the quadratic equation.

In this case ,  , and .

Now plug these values into the quadratic equation, and we get.

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.

The first step is to square each side of the inequality.

Now simplify each side.

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

Now we can use the quadratic formula.

Recall the quadratic formula.

Where , , and , correspond to coefficients in the quadratic equation.

In this case  ,  , and .

Now plug these values into the quadratic equation, and we get.

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.

The first step is to square each side of the inequality.

Now simplify each side.

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

Now we can use the quadratic formula.

Recall the quadratic formula.

Where , , and , correspond to coefficients in the quadratic equation.

In this case  ,  , and .

Now plug these values into the quadratic equation, and we get.

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.

The first step is to square each side of the inequality.

Now simplify each side.

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

Now we can use the quadratic formula.

Recall the quadratic formula.

Where , , and , correspond to coefficients in the quadratic equation.

In this case  ,  , and .

Now plug these values into the quadratic equation, and we get.

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.

The first step is to square each side of the inequality.

Now simplify each side.

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

Now we can use the quadratic formula.

Recall the quadratic formula.

Where , , and , correspond to coefficients in the quadratic equation.

In this case  ,  , and .

Now plug these values into the quadratic equation, and we get.

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.

The first step is to square each side of the inequality.

Now simplify each side.

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

Now we can use the quadratic formula.

Recall the quadratic formula.

Where , , and , correspond to coefficients in the quadratic equation.

In this case  ,  , and  .

Now plug these values into the quadratic equation, and we get.

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.