Quadratic Equations and Inequalities - Algebra 2

To solve by completing the square, you should first take the numerical coefficient to the “right side” of the equation:

Then, divide the middle coefficient by 2:

Square that and add it to both sides:

Now, you can easily factor the quadratic:

Take the square root of both sides:

Finish out the solution:

To solve by completing the square, you should first take the numerical coefficient to the “right side” of the equation:

Then, divide the middle coefficient by 2:

Square that and add it to both sides:

Now, you can easily factor the quadratic:

Take the square root of both sides:

Finish out the solution:

Make sure you keep track of negative signs when doing FOIL, especially when doing the Outer and Inner steps.

To solve by completing the square, you should first take the numerical coefficient to the “right side” of the equation:

Then, divide the middle coefficient by 2:

Square that and add it to both sides:

Now, you can easily factor the quadratic:

Take the square root of both sides:

Finish out the solution:

To solve by completing the square, you should first take the numerical coefficient to the “right side” of the equation:

Then, divide the middle coefficient by 2:

Square that and add it to both sides:

Now, you can easily factor the quadratic:

Take the square root of both sides:

Finish out the solution:

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Use a calculator to determine the final values.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Use a calculator to determine the final values.

To solve by completing the square, you should first take the numerical coefficient to the “right side” of the equation:

Then, divide the middle coefficient by 2:

Square that and add it to both sides:

Now, you can easily factor the quadratic:

Your next step would be to take the square root of both sides. At this point, however, you know that you cannot solve the problem. When you take the square root of both sides, you will be forced to take the square root of . This is impossible (at least in terms of real numbers), meaning that this problem must have no real solution.

In order to evaluate one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

Multiply terms by way of FOIL method.

Now multiply and simplify.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Separate this expression into two fractions and simplify to determine the final values.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Separate this expression into two fractions and simplify to determine the final values.

Multiply each term of the first trinomial by second trinomial.

Add and combine like-terms.

The answer is:

The expression will need to be rearranged from highest to lowest powers in order to be simplified.

Factor a 2 in the numerator.

Factor the term in parentheses.

Factor the denominator.

Divide the numerator with the denominator.

The expression becomes:

The answer is:

The correct answer is or . The first step of the problem is to cross multiply. This will give the following equation:

After subtracting from each side the equation looks like:

The expression on the right hand side can be factored into:

Both and satisfy the above equation and are therefore the correct answers.

Use the FOIL method (First, Outer, Inner, Last):

Put all of these terms together:

Combine like terms:

The discriminant is found using the formula . In this case:

To find the discriminant, use the formula . In this case:

To determine the amount of roots a given quadratic function has, we must find the discriminant, which for

is equal to

If d is negative, then we have two roots that are complex conjugates of one another. If d is positive, than we have two real roots, and if d is equal to zero, then we have only one real root.

Using our function and the formula above, we get

Thus, the function has only one real root.