George has a quadratic of the form x^2 + bx + 1/3, where b is a specific negative number. Using his knowledge of how to complete the square, George is able to rewrite this quadratic in the form (x + m)^2 + 1/10. What is b?
+37146 m will be 1/2 of b
2m = b
When completing the square yo wil have to subtract m^2 from the equation to keep it balanced
1/3 - m^2 = 1/10
- m^2 = 3/30 - 10/30
m^2 = 7/30
m = - sqrt 7/30 (we are told b is negative)
check : (x - sqrt (7/30) )^2 - 7/30 + 1/3 -7/30 + 10/30 = 1/10
x^2 - 2 sqrt(7/30) x + 7/30 - 7/30 + 1/3
x^2 - 2sqrt(7/30)x + 1/3
So b = 2m = - 2 sqrt (7/30)
