SOLUTION: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?

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Question 1180054: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?
Found 5 solutions by MathLover1, mananth, greenestamps, ikleyn, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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2x%5E2+%2B8x+-5=+0
%282x%5E2%2B8x%29-5=+0...factor out 2
2%28x%5E2%2B4x%29-5=+0
2%28x%5E2%2B4x%2Bb%5E2%29-2b%5E2-5=+0....b=4%2F2=2
2%28x%5E2%2B4x%2B2%5E2%29-2%2A2%5E2-5=+0
2%28x%2B2%29%5E2-8-5=+0
2%28x%2B2%29%5E2-13=+0
number should be added to the equation 13

Answer by mananth(16946) About Me  (Show Source):
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2 x^2 + 8 x - 5
divide by 2
x^2+4x =5
x^2 +4x +4 =5+4
x^2+4x +4 -9=0
-9 should be added

Answer by greenestamps(13203) About Me  (Show Source):
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The problem is poorly worded, so we don't really know what the question is that they are asking.

To begin with, you can't add a number to an equation without changing the equation. What you CAN do is add the SAME number to BOTH SIDES of an equation.

To complete a square, you need to factor out the coefficient of the leading term and then use the pattern

%28x%2Ba%29%5E2+=+x%5E2%2B2ax%2Ba%5E2

2x%5E2%2B8x-5=0
2x%5E2%2B8x=-5
2%28x%5E2%2B4x%29=-5

Using the pattern above, we have to add "+4" inside the parentheses. The expression in parentheses is being multiplied by 2, so we are adding 8 to the left side of the equation. So we can add 8 to BOTH SIDES of the equation to complete the square.

2%28x%5E2%2B4x%2B4%29=-5%2B8
2%28x%2B2%29%5E2=3

So with my interpretation of the question, the number I added TO BOTH SIDES OF THE EQUATION was 8.

Answer by ikleyn(52812) About Me  (Show Source):
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.

@greenestamps, your exposition is fine, but it still requires your corrections,
regarding the signs of different terms.



To the customer, who posted this question: 

    - definitely ignore the post by @mananth, since it contains 
      arithmetic errors and leads you to NOWHERE.


Also to the customer, for your better understanding. 

    There are two basic cases and two basic procedures when we complete the square.


    One case is when we transform a quadratic function to vertex form.


    Another case is when we solve quadratic equation by completing the square.


    These cases are different, and procedures are slightly different.


    For a beginner student, it is important to be informed about two cases 
    and different procedures, and to see and understand the difference.


    At least, to be WARNED about it . . .


On this subject,  see two my lessons in this site

    - HOW TO complete the square - Learning by examples
    - HOW TO solve quadratic equation by completing the square - Learning by examples


Two lessons are organized to teach you on these cases separately --- for your better understanding.



Answer by MathTherapy(10555) About Me  (Show Source):
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What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?
One person got 8, the other: - 9, and another, 13. They are ALL WRONG.

Correct answer: highlight_green%28-+8%29 needs to be added.