SOLUTION: Consider the equation, 4x^2-18x=3. What number must be added to both sides of the equation in order to complete the square?

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Question 1198731: Consider the equation, 4x^2-18x=3. What number must be added to both sides of the equation in order to complete the square?
Found 4 solutions by ikleyn, Alan3354, MathLover1, MathTherapy:
Answer by ikleyn(52785)   (Show Source): You can put this solution on YOUR website!
.
Consider the equation, 4x^2-18x=3. What number must be added
to both sides of the equation in order to complete the square?
~~~~~~~~~~~~~~~~ 

The leading term with  x^2  is  4x^2 = (2x)^2.


Therefore, you should add the term c^2, where you determine the value of "c" 
from this equality

    2*(2c) = -18,  which gives  c =  = -4  = -4.5.


The term to add to both sides is (-4.5)^2 = 20.25.    ANSWER

Solved.

---------------

On solving quadratic equations using completing the square method,  look into the lesson
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site.


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What Alan recommends in his post, is incorrect. 

The correct addend is  ,  referring to the general equation form

    ax^2 + bx = -c.


\\\\\\\\\\\\\\\\


Do not even read the post by @MathLover1, if you want to save your mind,

since her recommendation is totally wrong: it relates to the modified leading part equation,

while the problem asks about the addend to UNMODIFIED leading part equation.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Consider the equation, 4x^2-18x=3. What number must be added to both sides of the equation in order to complete the square?
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Add
===========================
NUM Lock wasn't on, the 2 got lost.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

The rule we use for completing the square is that if we add to both sides of the equation in order to complete the square.
But if a general quadratic equation have a coefficient of in front of :

we just divide the whole equation by "" first, then carry on:



............divide the whole equation by

............. the coefficient of the x term is , so , add to both sides




so, you need to add to both sides


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Consider the equation, 4x^2-18x=3. What number must be added to both sides of the equation in order to complete the square?
Correct number to be added: 

Accept NO OTHER answer!

As usual, anything MATHLOVER - Don't know how this name came about - says, it's advisable to do the opposite, ignore, or DUMP!!!
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