2n^2+12n+10=0 complete the square

2n² + 12n + 10 = 0

n = - 12 + / - √ (12² - 4 (2) (10))

2 (2)

n = - 12 + / - √ (144 - 80)

4

n = - 12 + / - √64

4

n = - 12 + / - 8

4

n = - 12 + 8 n = - 12 - 8

4 4

n = - 4 n = - 20

4 4

n = - 1 n = - 5

Simplify the equation into a proper form to complete the square.

2 n^2 + 12n=-10

Divide each term in the equation by 2.

n^2 + 6n=-5

To create a trinomial square on the left-hand side of the equation, find a value that is equal to the square of half of b, the coefficient of n.

(b/2) ^2 = (3) ^2

Add the term to each side of the equation.

n^2 + 6n + (3) ^2 = - 5 + (3) ^2

Simplify the equation.

n^2 + 6n+9=4

Factor the perfect trinomial square into (n+3) ^2.

(n+3) ^2 = 4

Solve the equation for n.

n=-1,-5