SOLUTION: Pls help struggling to help ny daughter the question is If the square number of a positive is increased by 3 times the number, the result is 54.find the number
Question 1079735: Pls help struggling to help ny daughter the question is If the square number of a positive is increased by 3 times the number, the result is 54.find the number Found 3 solutions by josmiceli, addingup, MathTherapy:Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website! Did I understand this right?
The square of a positive number is increased
by 3 times that number, and the result is 54
OK?
----------------------------
Let the unknown positive number =
given:
Subtract from both sides
This is a quadratic equation, and it has to
be factored. Then you will have 2 solutions
for
The form ofthe solution will look like this:
where and are unkown for the moment
Notice that . and will be my and
---------------------------------------
Now expand the left side
------------------------------
In order for the left side to be true, either or
You are looking for a positive number, so the
answer is
---------------------------------------
check answer:
Square the number:
-------------------
Now add 3 times that number
which is correct
Hope this helps
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website! Solving by factoring
--------------------------
x^2+(3x) = 54
The coefficient of x is 3. Take 1/2 of the coefficient, square it, and add it to both sides: 3/1/2 = 3/2; 3/2^2 = 9/4 now add this to both sides:
x^2+3x+9/4 = 225/4
Now we can write the left side as a square:
(x+3/2)^2 = 225/4
take the sqrt both sides and we have two possible answers:
x+3/2 = 15/2 or x+3/2 = -15/2
now solve for x, one equation at a time:
x+3/2-3/2 = 15/2-3/2
x = 12/2 = 6
Next:
x+3/2 = -15/2 subtract 3/2 from both sides
x = -18/2 = -9
We are not looking for a negative number, so let's try 6:
6^2+(3*6) = 54
36+18 = 54 how do you know, we got the right answer ;-)
:
John
Let the number be N
Then we get: ------ Subtracting 54 from both sides
(N - 6)(N + 9) = 0 ------ Factoring TRINOMIAL on left
N - 6 = 0 OR N + 9 = 0
N, or number = OR N = - 9 (ignore as this is NEGATIVE)