Question 97771: Hi!! How do you solve this equation as a quadratic equation????? Found 2 solutions by Msgenes, checkley71:Answer by Msgenes(10) (Show Source):
You can put this solution on YOUR website! Which method are you supposed to use? Completing the square or using the quadratic formula.
I am using the completing the square method.
3x^2 = 10x
We have to get the 10x on the other side and we do that by substracting 10x on both sides
3x^2 - 10x = 10x -10x
3x^2 - 10x = 0
Now we need x^2 to be by itself and we do that by dividing by 3.
3x^2 - 10x = 0
..............
3 3
x^2 - 10x = 0
....
3
Now we are able to complete the square by taking half 0f 10x/3 in other words divid 10x/3 by 2 then we square it.
(10x/3)/2 = (5/3)^2 = 25/9
Now we add 25/9 to both sides.
x^2 - 10x + 25 = 25
.............
3 9 9
Now we have to factor this out.
(x - 5/3)^2 = 25/9
Now we take the square root on both sides.
Sqrt(x - 5/3)^2 = Sqrt 25/9
We will have two solutions.
x - 5/3 = 5/3
So here again we need to get x by itself and we do that by adding 5/3 on both sides.
x - 5/3 + 5/3 = 5/3 + 5/3
x = 10/3
For the second solution we will do the opposite of the first one.
x + 5/3 = 5/3
x + 5/3 - 5/3 = 5/3 - 5/3
x = 0
Normally the problem would be written using the plus or minus sign. And that is completing the Square. I hopes this helps. Good Luck. :)
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