SOLUTION: Completing the Square What is half of -4y/3 squared? 3y^2-4y-1=0 3y^2/3-4y/3-1/3=0/3 y^2-4y/3=1/3 This is where I get stuck. I'm supposed to take half of -4y/3 and s

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Completing the Square What is half of -4y/3 squared? 3y^2-4y-1=0 3y^2/3-4y/3-1/3=0/3 y^2-4y/3=1/3 This is where I get stuck. I'm supposed to take half of -4y/3 and s      Log On


   

Question 736993: Completing the Square
What is half of -4y/3 squared?
3y^2-4y-1=0
3y^2/3-4y/3-1/3=0/3
y^2-4y/3=1/3 This is where I get stuck.
I'm supposed to take half of -4y/3 and square it.
I'm not quite understanding how to do it. Do you square both -4 and 3 separately? Then it becomes -16y/9?
If you halve it, it becomes -2y/1.5?? Should you not have a decimal or a fraction?

Found 2 solutions by fcabanski, josmiceli:
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Only square half of the coefficient of the y term. Half of -4/3 is -2/3. Square both the numerator and denominator. -2/3 squared is 4/9.


y%5E2-4y%2F3+%2B+4%2F9+=1%2F3+%2B+4%2F9


y%5E2-4y%2F3+%2B+4%2F9+=7%2F9


%28y-2%2F3%29%5E2+=+7%2F9


y - 2/3 = + or - sqrt%287%2F9%29 = + or - sqrt%287%29%2F3%29
y = (2 + or - sqrt%287%29)/3

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3y%5E2+-+4y+-+1+=+0+
+3y%5E2+-+4y+=+1+
+y%5E2+-+%284%2F3%29%2Ay+=+1%2F3+
In this equation, which is for finding the roots,
+y+ is called the independent variable.
-------------------
It would be plotted on the horizontal axis,
which is normally the +x+ axis.
-------------------
The rule for completing the square is:
Take 1/2 of the co-efficient of the +y+
term ( usually called the +x+ term ),
square it, then add it to both sides
-------------------
The co-efficient of the +y+ term is
+-4%2F3+, so
+%28-4%2F3%29+%2F+2+=+-4%2F6+
+-4%2F6+=+-2%2F3+
Now square it
+%28-2%2F3+%29%5E2+=+4%2F9+
Add it to both sides
+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+1%2F3+%2B+4%2F9+
+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+3%2F9+%2B+4%2F9+
+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+7%2F9+
+%28+y+-+2%2F3+%29%5E2+=+%28+sqrt%287%29+%2F+3+%29%5E2+
Take the square root of both sides
+y+-+2%2F3+=+sqrt%287%29+%2F+3+
+y+=+%28+2+%2B+sqrt%287%29+%29+%2F+3+
and
+y+=+%28+2+-+sqrt%287%29+%29+%2F+3+
------------------------
Here's a plot of the entire equation, which can
be expressed as +z+=+3y%5E2+-+4y+-+1+
Note that +sqrt%287%29+=+2.6458+
+%28+2+%2B+2.6458+%29+%2F+3+=+1.5486+ and
+%28+2+-+2.6458+%29+%2F+3+=+-.2153+
You can see that these are the horizontal axis crossings
( Unless I messed up )
+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+6%2C+3x%5E2+-+4x+-+1+%29+