Solve Each Equation by completing the square... n² + 6n + 9=7

Question

I do know the formula C=(B/2)²

Answer 1

n² + 6n + 9 = 7

 

as you said:  c = (b/2)²

b = 6

b/2 = 3

(b/2)² = 9

 

n² + 6n + 9 = (n+3)²

 

(n+3)² = 7

take square root of both sides

(n+3) = ±√7

 

n = -3 ±√7

 

n = {-3 - √7,  -3 + √7}

Answer 2

n² + 6n + 9 = 7

n² + 6n = -2

 

Apply c² = (b/2)², where b=6.  Since we add (6/2)² to the right side of the equation, we need to add it to the right side as well to keep things equal.

 

n² + 6n + (6/2)² = -2 + (6/2)²

n² + 6n + 9 = -2 + 9

(n + 3)² = 7

n + 3 = ±√7

 

n = -3 ± √7

 

Check by plugging n = -3+√7 into the equation to see if you end up with 7=7.  Then try -3-√7.