### All College Algebra Resources

## Example Questions

### Example Question #1 : How To Find A Solution Set

Give all real solutions of the following equation:

**Possible Answers:**

**Correct answer:**

By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:

We are looking to factor the quadratic expression as , replacing the two question marks with integers with product and sum 5; these integers are .

Substitute back:

The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:

Set each factor to zero and solve:

Since no real number squared is equal to a negative number, no real solution presents itself here.

The solution set is .

### Example Question #11 : How To Find A Solution Set

Give all real solutions of the following equation:

**Possible Answers:**

The equation has no real solutions.

**Correct answer:**

By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:

We are looking to factor the quadratic expression as , replacing the two question marks with integers with product 36 and sum ; these integers are .

Substitute back:

These factors can themselves be factored as the difference of squares:

Set each factor to zero and solve:

The solution set is .

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