SOLUTION: what should be added with 3x^2 + 5x to make it perfect square?

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Question 884588: what should be added with 3x^2 + 5x to make it perfect square?
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.