Example Questions

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Example Question #405 : Algebra

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 #406 : Algebra

What are the roots of

or

or

or

or

Explanation:

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

or

Example Question #11 : Solving By Other Methods

Solve the following by using the Quadratic Formula:

No solution

Explanation:

Plugging into the Quadratic Formula, we get

*The square root of a negative number will involve the use of complex numbers

Therefore,

Example Question #408 : Algebra

A rectangular yard has a width of w and a length two more than three times the width. The area of the yard is 120 square feet. Find the length of the yard.

5 feet

20 feet

89 feet

6 feet

24 feet

20 feet

Explanation:

The area of the garden is 120 square feet. The width is given by w, and the length is 2 more than 3 times the width. Going by the order of operations implied, we have length given by 3w+2.

(length) x (width) = area (for a rectangle)

In order to solve for w, we need to set the equation equal to 0.

To solve this we should use the Quadratic Formula:

(reject)

The width is 6 feet, so the length is  or 20 feet.

Example Question #401 : Algebra

Complete the square to solve for  in the equation

or

Explanation:

1) Get all of the variables on one side and the constants on the other.

2) Get a perfect square trinomial on the left side. One-half the x-term, which will be squared. Add squared term to both sides.

3) We have a perfect square trinomial on the left side

4)

5)

6)

7)

8)

9)

Example Question #410 : Algebra

Solve the following quadratic equation for x by completing the square:

or

or

or

or

Explanation:

This quadratic equation needs to be solved by completing the square.

1) Get all of the x-terms on the left side, and the constants on the right side.

2) To put this equation into terms are more common with completing the square, we can make a coefficient of 1 in front of the  term.

3) We need to make the left side of the equation into a "perfect square trinomial." To do this, we take one-half of the coefficient in front of the x, square it, and add it to both sides.

The left side is a perfect square trinomial.

4) We can represent a perfect square trinomial as a binomial squared.

5) Take the square root of both sides

6) Solve for x

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