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

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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) About Me  (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 = +x+
given:
+x%5E2+%2B+3x+=+54+
Subtract +54+ from both sides
+x%5E2+%2B+3x+-+54+=+0+
This is a quadratic equation, and it has to
be factored. Then you will have 2 solutions
for x
The form ofthe solution will look like this:
+%28+x+%2B+j+%29%2A%28+x+-+k+%29+=+0+
where j and k are unkown for the moment
Notice that +54+=+6%2A9+.
6 and +9+ will be my j and k
---------------------------------------
+%28+x+%2B+9+%29%2A%28+x+-+6+%29+=+0+
Now expand the left side
+x%5E2+%2B+9x+-+6x+-+54+=+0+
+x%5E2+%2B+3x+-+54+=+0+
------------------------------
In order for the left side to be true, either
+x+=+6+ or
+x+=+-9+
You are looking for a positive number, so the
answer is +x+=+6+
---------------------------------------
check answer:
Square the number:
+x%5E2+=+6%5E2+
+x%5E2+=+36+
-------------------
Now add 3 times that number
+36+%2B+3%2A6+=+36+%2B+18+
+36+%2B+18+=+54+
which is correct
Hope this helps

Answer by addingup(3677) About Me  (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




Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
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 
Let the number be N

Then we get: N%5E2+%2B+3N+=+54

N%5E2+%2B+3N+-+54+=+0 ------ Subtracting 54 from both sides

(N - 6)(N + 9) = 0 ------ Factoring TRINOMIAL on left

N - 6 = 0     OR      N + 9 = 0

N, or number = highlight_green%286%29     OR       N = - 9 (ignore as this is NEGATIVE)