4n^2=-12n-6

Question

find or approximate solutions to the eqiation...round to three decimal places

Answer 1

bring all terms to one side and set equal to 0

4n²+12n+6=0

factor out 2

2(2n²+6n+3)=0 ===> 2n²+6n+3=0  

complete the square

2(n²+3n+9/4) + 3 = 0 + 9/2 ===> 2(n+3/2)² = 3/2 ===> (n+3/2)² = 3/4

take square root of both sides

(n+3/2)=±√3/2

solve for n

n = (-3+√3)/2 = -0.634 or n = (-3-√3)/2 = -2.366