# GED Math : Quadratic Equations

## Example Questions

### Example Question #7 : Simplifying Quadratics

Simplify the following expression:

Explanation:

Start by factoring the numerator.

To factor the numerator, you will need to find  numbers that add up to  and multiply to .

Next, factor the denominator.

To factor the denominator, you will need to find two numbers that add up to  and multiply to .

Rewrite the fraction in its factored form.

Since  is found in both numerator and denominator, they will cancel out.

### Example Question #8 : Simplifying Quadratics

Simplify:

Explanation:

We need to factor both the numerator and the denominator to determine what can cancel each other out.

If we factor the numerator:

Two numbers which add to 6 and multiply to give you -7.

Those numbers are 7 and -1.

If we factor the denominator:

First factor out a 2

Two numbers which add to -4 and multiply to give you 3

Those numbers are -3 and -1

Now we can re-write our expression with a product of factors:

We can divide  and  to give us 1, so we are left with

### 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, .

Add this to both sides:

### Example Question #81 : Quadratic Equations

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 #1 : 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 #401 : Algebra

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 #402 : Algebra

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

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.

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:

x = 10 or x = -17

x = -8.5

x = -5 or x = 8.5

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