Answer :
Simplify the equation into a proper form to complete the square.
2n^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
2n^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
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
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
