SOLUTION: Hi, Can I get help with this question This polynomial is factorable, so you should be able to find the roots without using the complete the square method. However we're going t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, Can I get help with this question This polynomial is factorable, so you should be able to find the roots without using the complete the square method. However we're going t      Log On


   

Question 1153798: Hi,
Can I get help with this question
This polynomial is factorable, so you should be able to find the roots without using the complete the square method.
However we're going to walk through the process of completing the square as practice for those polynomials where you cannot use the factoring method

Solve the equation for x
x^(2)+6x-27=0
Step 1: Separate term fro the variables
Step 2: Complete the square
Step 3: Factor the complete square
Step 4: Use the Square Root Property
Step 5: Finish solving
Thank you.
Margaret
Found 3 solutions by Alan3354, ikleyn, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 6x - 27 = 0
x^2 + 6x = 27
x^2 + 6x + 9 = 27 + 9 = 36
(x+3)^2 = 36
x+3 = 6
x = 3
=================
x+3 = -6
x = -9


Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

Learn the subject from the scratch (as you need it (!) ) from the lessons
    - HOW TO complete the square - Learning by examples
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic  "Quadratic equations".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2+%2B+6x+-+27+=+0

Step 1: Separate term from the variables
%28x%5E2+%2B+6x%29+-+27+=+0
Step 2: Complete the square
%28x%5E2+%2B+6x%2Bb%5E2%29-b%5E2+-+27+=+0......since coefficient a=1 and 2ab=6=>b=3
%28x%5E2+%2B+6x%2B3%5E2%29-3%5E2+-+27+=+0
%28x%2B3%29%5E2-9+-+27+=+0
%28x%2B3%29%5E2-36+=+0


Step 3: Factor the complete square
%28x%2B3%29%5E2-36+=+0.....write 36 as 6%5E2
%28x%2B3%29%5E2-6%5E2+=+0
%28x%2B3%29%5E2=6%5E2+


Step 4: Use the Square Root Property
%28x%2B3%29%5E2=6%5E2+
x%2B3=sqrt%286%5E2%29+
x=sqrt%286%5E2%29-3+
Step 5: Finish solving
x=sqrt%286%5E2%29-3+=>x=6-3+=>x=3
x=sqrt%286%5E2%29-3+=>x=-6-3+=>x=-9