GED Math : Solving by Other Methods

Example Questions

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Example Question #1 : Solving By Other Methods

Solve for  by completing the square:

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, .

Example Question #2 : Solving By Other Methods

Solve for :

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 #3 : Solving By Other Methods

Solve for :

or

or

or

or

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 #4 : Solving By Other Methods

Solve for :

or

or

or

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 #5 : Solving By Other Methods

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

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 #6 : Solving By Other Methods

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

Explanation:

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

and

Example Question #7 : Solving By Other Methods

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

Explanation:

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:

x = -5 or x = 8.5

x = -8.5

x = 10 or x = -17

x = 5

x = 5 or x= -8.5

x = 5 or x= -8.5

Explanation:

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:

or

or

or

or

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 #10 : Solving By Other Methods

What are the roots of

or

or

or

or

Explanation:

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

or

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