Question 1198731
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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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<pre>
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 = {{{-18/(2*2)}}} = -4{{{1/2}}}  = -4.5.


The term to add to both sides is (-4.5)^2 = 20.25.    <U>ANSWER</U>
</pre>

Solved.


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-solve-quadratic-equation-by-completing-the-square-Learning-by-examples.lesson>HOW TO solve quadratic equation by completing the square - Learning by examples</A> 

in this site.



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What Alan recommends in his post, is incorrect.


<pre>
The correct addend is  {{{b^2/(4a)}}},  referring to the general equation form

    ax^2 + bx = -c.
</pre>


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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.