3n^2+9n+10=2

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Solution for 3n^2+9n+10=2 equation:


Simplifying
3n2 + 9n + 10 = 2

Reorder the terms:
10 + 9n + 3n2 = 2

Solving
10 + 9n + 3n2 = 2

Solving for variable 'n'.

Reorder the terms:
10 + -2 + 9n + 3n2 = 2 + -2

Combine like terms: 10 + -2 = 8
8 + 9n + 3n2 = 2 + -2

Combine like terms: 2 + -2 = 0
8 + 9n + 3n2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2.666666667 + 3n + n2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 3n + -2.666666667 + n2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 3n + n2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 3n + n2 = 0 + -2.666666667
3n + n2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
3n + n2 = -2.666666667

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = -2.666666667 + 2.25

Reorder the terms:
2.25 + 3n + n2 = -2.666666667 + 2.25

Combine like terms: -2.666666667 + 2.25 = -0.416666667
2.25 + 3n + n2 = -0.416666667

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = -0.416666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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