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Example Questions
Example Question #1 : Solving By Other Methods
Solve for by completing the square:
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 :
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
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
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 ?
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 #1 : Solving By Other Methods
What is the solution to the equation ? Round your answer to the nearest tenths place.
Recall the quadratic equation:
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.
Solve this equation by using the quadratic equation:
For the equation ,
Plug it in to the equation to solve for .
and
Example Question #1 : Solving By Other Methods
Solve for x by using the Quadratic Formula:
x = 5
x = 10 or x = -17
x = -5 or x = 8.5
x = 5 or x= -8.5
x = -8.5
x = 5 or x= -8.5
We have our quadratic equation in the form
The quadratic formula is given as:
Using
Example Question #2 : Solving By Other Methods
Solve the following for x by completing the square:
or
or
or
or
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 #1 : Solving By Other Methods
What are the roots of
or
or
or
or
involves rather large numbers, so the Quadratic Formula is applicable here.
or
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