To determine the nature of the solution set of a quadratic equation, it is necessary to first express it in standard form 

To accomplish this, first, multiply the binomials on the left using the FOIL technique:

Collect like terms:

Now, add 18 to both sides:

The key to determining the nature of the solution set is to examine the discriminant . Setting , the value of the discriminant is 

This discriminant is negative. Consequently, the solution set comprises two imaginary numbers.

To determine the nature of the solution set of a quadratic equation, it is necessary to first express it in standard form 

This can be done by switching the first and third terms on the left:

The key to determining the nature of the solution set is to examine the discriminant 

. Setting , the value of the discriminant is

.

The discriminant is a positive number but not a perfect square. Therefore, there are two irrational solutions.

The first step to solving an equation where  is in a radical is to isolate the radical. To do this, we need to subtract the 5 from both sides.

Now that the radical is isolated, clear the radical by raising both sides to the power of 3. Note:

Now we want to isolate the  term. First, subtract the 5 from both sides.

Finally, divide both sides by  to solve for .

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

Multiply both sides by :

Subtract  from both sides:

Multiply both sides by , distributing on the right:

,

the correct response.

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

Subtract  from both sides:

Divide both sides by 9:

Take the square root of both sides:

Simplify the expression on the right by splitting it, and taking the square root of numerator and denominator:

,

the correct response.

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

First, take the reciprocal of both sides:

Multiply both sides by :

Distribute on the right:

Subtract 1 from both sides, rewriting 1 as to facilitate subtraction:

,

the correct response.

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

Subtract 20 from both sides:

Divide both sides by :

,

the correct response.

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

First, add  to both sides:

Take the positive square root of both sides:

,

the correct response.

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

First, square both sides to eliminate the radical symbol:

Rewrite the expression on the right using the square of a binomial pattern:

Subtract 1 from both sides:

,

the correct response.