<PRE><B>Question 884588</B>
to convert 3x^2 + 5x into an equivalent perfect square form, you have to do the following:


factor out the 3 to get 3 * (x^2 + (5/3)x)


take half the coefficient of the x term to get (5/6).


you will get the perfect square expression of 3 * (x + (5/6))^2


if you square (x + (5/6))^2, your expression will become:


3 * (x^2 + 2*(5/6)x + (5/6)^2).


simplify this by distributing the factor of 3 to get:


3x^2 + 3*2*(5/6)x + 3*(5/6)^2 which simplifies to:


3x^2 + 5x + 75/36


this simplifies further to:


3x^2 + 5x + 25/12 whose perfect square form is 3 * (x + (5/6))^2


if these form are equivalent, they will give you the same answer regardless of the value of x.


i chose x = 5 to test this out.


i got:


3x^2 + 5x + 25/12 = 102.08333....


3 * (x + 5/6)^2 = 102.08333....


since the answers are the same, this  confirms the expressions are equivalent.











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