SOLUTION: I thought the last solution (to subtract 8 from each side) was what my teacher wanted, but they're actually asking me to "Solve by completing the square" for this equation: 9x^2+6x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I thought the last solution (to subtract 8 from each side) was what my teacher wanted, but they're actually asking me to "Solve by completing the square" for this equation: 9x^2+6x      Log On


   

Question 1058267: I thought the last solution (to subtract 8 from each side) was what my teacher wanted, but they're actually asking me to "Solve by completing the square" for this equation: 9x^2+6x=8
Thank you!
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


9x%5E2%2B6x=8

Divide thru by 9, the coefficient of the 
term in x%5E2

%289%2F9%29x%5E2%2B%286%2F9%29x=8%2F9

x%5E2%2B%282%2F3%29x=8%2F9

To the side, multiply the coefficient of x by 1%2F2.
%282%2F3%29%281%2F2%29=1%2F3

Now square 1%2F3.  %281%2F3%29%5E2=1%2F9

Add 1%2F9 to both sides of

x%5E2%2B%282%2F3%29x%2B1%2F9=8%2F9%2B1%2F9

Combine the right side: 8%2F9%2B1%2F9=9%2F9=1

x%5E2%2B%282%2F3%29x%2B1%2F9=1

Factor the left side:

%28x%2B1%2F3%29%28x%2B1%2F3%29=1

Write the left side as the square of
a binomial:

%28x%2B1%2F3%29%5E2=1

Take the square root of both sides,
remembering the ± on the right:

sqrt%28%28x%2B1%2F3%29%5E2%29+=+%22%22+%2B-sqrt%281%29

x%2B1%2F3+=+%22%22+%2B-+1

x=-1%2F3+%2B-+1

Using the +

x=-1%2F3+%2B+1
x=-1%2F3+%2B+3%2F3
x=2%2F3

Using the -

x=-1%2F3+-+1
x=-1%2F3+-+3%2F3
x=-4%2F3

The solutions are 2%2F3 and -4%2F3

Edwin

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+9x%5E2+%2B+6x+=+8+
Divide both sides by +9+
+x%5E2+%2B+%282%2F3%29%2Ax+=+8%2F9+
Take 1/2 of the coefficient of the x
term, square it, and add it to both sides
+x%5E2+%2B+%282%2F3%29%2Ax+%2B+%281%2F3%29%5E2+=+8%2F9+%2B+%281%2F3%29%5E2+
+x%5E2+%2B+%282%2F3%29%2Ax+%2B+1%2F9+=+8%2F9+%2B+1%2F9+
+x%5E2+%2B+%282%2F3%29%2Ax+%2B+1%2F9+=+1%0D%0A%7B%7B%7B+%28+x+%2B+1%2F3+%29%5E2+=+1%5E2+
Take the square root of both sides
+x+%2B+1%2F3+=+1+
+x+=+2%2F3+
and, taking the negative square root of +1%5E2+,
+x+%2B+1%2F3+=+-1+
+x+=+-4%2F3+
-------------------
check the solutions:
+%28+x+-+2%2F3+%29%2A%28+x+%2B+4%2F3+%29=+0+
+x%5E2+-+%282%2F3%29%2Ax+%2B+%284%2F3%29%2Ax+-+8%2F9+=+0+
+x%5E2+%2B+%282%2F3%29%2Ax+-+8%2F9+=+0+
Multiply both sides by +9+
+9x%5E2+%2B+6x+-+8+=+0+
+9x%5E2+%2B+6x+=+8+
OK