n^2+3n+40=0

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Solution for n^2+3n+40=0 equation:


Simplifying
n2 + 3n + 40 = 0

Reorder the terms:
40 + 3n + n2 = 0

Solving
40 + 3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 3n + -40 + n2 = 0 + -40

Reorder the terms:
40 + -40 + 3n + n2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 3n + n2 = 0 + -40
3n + n2 = 0 + -40

Combine like terms: 0 + -40 = -40
3n + n2 = -40

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 = -40 + 2.25

Reorder the terms:
2.25 + 3n + n2 = -40 + 2.25

Combine like terms: -40 + 2.25 = -37.75
2.25 + 3n + n2 = -37.75

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = -37.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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