### All GED Math Resources

## Example Questions

### Example Question #1 : Solving By Other Methods

Solve for by completing the square:

**Possible Answers:**

**Correct answer:**

To complete the square, we have to add a number that makes the left side of the equation a perfect square. Perfect squares have the formula .

In this case, .

Add this to both sides:

### Example Question #2 : Solving By Other Methods

Solve for :

**Possible Answers:**

**Correct answer:**

can be demonstrated to be a perfect square polynomial as follows:

It can therefore be factored using the pattern

with .

We can rewrite and solve the equation accordingly:

This is the only solution.

### Example Question #3 : Solving By Other Methods

Solve for :

**Possible Answers:**

or

or

or

or

**Correct answer:**

or

When solving a quadratic equation, it is necessary to write it in standard form first - that is, in the form . This equation is not in this form, so we must get it in this form as follows:

We factor the quadratic expression as

so that and .

By trial and error, we find that

, so the equation becomes

Set each linear binomial to 0 and solve separately:

The solution set is .

### Example Question #4 : Solving By Other Methods

Solve for :

**Possible Answers:**

or

or

or

**Correct answer:**

or

When solving a quadratic equation, it is necessary to write it in standard form first - that is, in the form . This equation is not in this form, so we must get it in this form as follows:

We factor the quadratic expression as

so that and .

By trial and error, we find that

, so the equation becomes

.

Set each linear binomial to 0 and solve separately:

The solutions set is

### Example Question #1 : Solving By Other Methods

Rounded to the nearest tenths place, what is solution to the equation ?

**Possible Answers:**

**Correct answer:**

Solve the equation by using the quadratic formula:

For this equation, . Plug these values into the quadratic equation and to solve for .

and

### Example Question #6 : Solving By Other Methods

What is the solution to the equation ? Round your answer to the nearest tenths place.

**Possible Answers:**

**Correct answer:**

Recall the quadratic equation:

For the given equation, . Plug these into the equation and solve.

and

### Example Question #2 : Solving By Other Methods

What is the solution to the equation ? Round your answer to the nearest hundredths place.

**Possible Answers:**

**Correct answer:**

Solve this equation by using the quadratic equation:

For the equation ,

Plug it in to the equation to solve for .

and

### Example Question #8 : Solving By Other Methods

Solve for x by using the Quadratic Formula:

**Possible Answers:**

x = 5 or x= -8.5

x = 5

x = 10 or x = -17

x = -8.5

x = -5 or x = 8.5

**Correct answer:**

x = 5 or x= -8.5

We have our quadratic equation in the form

The quadratic formula is given as:

Using

### Example Question #9 : Solving By Other Methods

Solve the following for x by completing the square:

**Possible Answers:**

or

or

or

or

**Correct answer:**

or

To complete the square, we need to get our variable terms on one side and our constant terms on the other.

1)

2) To make a perfect square trinomial, we need to take one-half of the x-term and square said term. Add the squared term to both sides.

3) We now have a perfect square trinomial on the left side which can be represented as a binomial squared. We should check to make sure.

* (standard form)

In our equation:

(CHECK)

4) Represent the perfect square trinomial as a binomial squared:

5) Take the square root of both sides:

6) Solve for x

or

### Example Question #10 : Solving By Other Methods

What are the roots of

**Possible Answers:**

or

or

or

**Correct answer:**

or

involves rather large numbers, so the Quadratic Formula is applicable here.

or