SOLUTION: what is it that people divide by when they get to the second step can someone show me in this example with work and solution. By completing the square, the expression x^2-

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: what is it that people divide by when they get to the second step can someone show me in this example with work and solution. By completing the square, the expression x^2-      Log On


   

Question 622029: what is it that people divide by when they get to the second step can someone show me in this example with work and solution.


By completing the square, the expression x^2-12 x +198 equals (x+A)^2+B
where A = and B =
Found 2 solutions by josmiceli, jessica43:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Set expression to 0 to find roots
+x%5E2+-+12x+%2B+198+=+0+
First subtract +198+ from both sides
+x%5E2+-+12x+=+-198+
To complete the square, take 1/2 of the
coefficient of the x term, then square
it, then add it to both sides
+x%5E2+-+12x+%2B+%28-12%2F2%29%5E2+=+-198+%2B+%28-12%2F2%29%5E2+
+x%5E2+-+12x+%2B+36+=+-198+%2B+36+
+%28+x+-+6+%29%5E2+=+-162+
Add +162+ to both sides
+%28+x+-+6+%29%5E2+%2B+162+=+0+
check:
Does the left side = +x%5E2+-+12x+%2B+198+ ?
+%28+x+-+6+%29%5E2+%2B+162+=+x%5E2+-+12x+%2B+36+%2B+162+
++x%5E2+-+12x+%2B+36+%2B+162+=+x%5E2+-+12x+%2B+198+
OK, so
+%28x+%2B+A%29%5E2+%2B+B+=+%28+x+-+6+%29%5E2+%2B+162+
+A+=+-6+
+B+=+162+


Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
To complete the square, follow these steps.
First you want to move the "loose" number to the other side of the equation:
x^2 - 12x + 198
x^2 - 12x = -198
Next, you want to take half of the x-term (that is, divide it by two) and square it. So in this case, take -12, divide it by 2 (-6) and then square that ((-6)^2=36). Add this square to both sides of the equation.
x^2 - 12x = -198
x^2 - 12x + 36 = -198 + 36
x^2 - 12x + 36 = -162
Finally, convert the left-hand side to squared form. To find the value "A" of the squared form, take the square root of the "loose" number on the left side of the equation, in our case, 36 (sqrt(36) = +/-6). Be careful of the sign. To know whether it is +6 or -6, look at the middle x-term (-12x). We need A + A = -12. So -6 is the answer.
x^2 - 12x + 36 = -162
(x - 6)^2 = -162
(x - 6)^2 + 162
So your answer is (x-6)^2 + 162.