GED Math : Solving by Other Methods

Study concepts, example questions & explanations for GED Math

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Example Questions

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Example Question #1 : Solving By Other Methods

Solve for  by completing the square:

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

 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 #83 : Quadratic Equations

Solve for :

Possible Answers:

 or 

 or 

 or 

 or 

Correct answer:

 or 

Explanation:

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 #3 : Solving By Other Methods

Solve for :

Possible Answers:

 or 

 or 

 or 

Correct answer:

 or 

Explanation:

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 #401 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

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 #402 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

Recall the quadratic equation:

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

and

Example Question #403 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

Solve this equation by using the quadratic equation:

For the equation 

Plug it in to the equation to solve for .

 and 

 

Example Question #404 : Algebra

Solve for x by using the Quadratic Formula:

 

Possible Answers:

x = 5

x = 10 or x = -17

x = 5 or x= -8.5

x = -5 or x = 8.5

x = -8.5

Correct answer:

x = 5 or x= -8.5

Explanation:

We have our quadratic equation in the form 

The quadratic formula is given as:

Using 

                        

                                   

                                       

Example Question #405 : Algebra

Solve the following for x by completing the square:

Possible Answers:

 or 

 or 

 or 

 or 

Correct answer:

 or 

Explanation:

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 #406 : Algebra

What are the roots of 

Possible Answers:

 or

 or 

 or 

Correct answer:

 or 

Explanation:

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

         or         

                                  

                                    

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