Lulu has a quadratic of the form x^2+bx+44, where b is a specific positive number. Using her knowledge of how to complete the square, Lulu is able to rewrite this quadratic in the form (x+m)^2+8. What is b?
+23248 x2 + bx + 44 = (x + m)2 + 8
x2 + bx + 44 = [(x + m)(x + m)] + 8
x2 + bx + 44 = x2 + 2mx + m2 + 8
Subtracting x2 from both sides:
bx + 44 = 2mx + m2 + 8
The x-term on the left-side equals the x-term on the right side: bx = 2mx
The number term on the left-side equals the number terms on the right-side: 44 = m2 + 8
Solving: 44 = m2 + 8 for the positive value of m:
36 = m2
---> m = 6
Placing this value of m into the equation: bx = 2mx
---> bx = 2(6)x
---> bx = 12x
---> b = 12
