SOLUTION: What must be added to 3x^2 -12x to make it a perfect square?

Algebra ->  Equations -> SOLUTION: What must be added to 3x^2 -12x to make it a perfect square?      Log On


   

Question 1120847: What must be added to 3x^2 -12x to make it a perfect square?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3x%5E2+-+12x+=+%28+ax+-+b+%29%5E2+
+3x%5E2+-+12x+=+a%5E2%2Ax%5E2+-+2a%2Ab%2Ax+%2B+b%5E2+
+a%5E2+=+3+
+a+=+sqrt%283%29+
+-2a%2Ab+=+-12+
+-2%2Asqrt%283%29%2Ab+=+-12+
+b+=+6%2Fsqrt%283%29+
+b%5E2+=+36%2F3+
+b%5E2+=+12+
Add +12+ to make it a perfect square
+%28+sqrt%283%29x+-+sqrt%2812%29+%29%5E2+=+3x%5E2+-+12x+%2B+12+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
What must be added to 3x^2 -12x to make it a perfect square?
3x%5E2+-+12 ====> 3%28x%5E2+-+4%29 =====> 3%28x%5E2+-+4+%2B+%28%28%221%22%2F%222%22%29+%2A+-+4%29%5E2%29%29%29 =====> 3%28x%5E2+-+4x+%2B+4%29 =====> 3x%5E2+-+12+%2B+12

As seen, 12 MUST be ADDED.