7n^2=-6n-7

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Solution for 7n^2=-6n-7 equation:


Simplifying
7n2 = -6n + -7

Reorder the terms:
7n2 = -7 + -6n

Solving
7n2 = -7 + -6n

Solving for variable 'n'.

Reorder the terms:
7 + 6n + 7n2 = -7 + -6n + 7 + 6n

Reorder the terms:
7 + 6n + 7n2 = -7 + 7 + -6n + 6n

Combine like terms: -7 + 7 = 0
7 + 6n + 7n2 = 0 + -6n + 6n
7 + 6n + 7n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
7 + 6n + 7n2 = 0

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

Divide each side by '7'.
1 + 0.8571428571n + n2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.8571428571n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + 0.8571428571n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.8571428571n + n2 = 0 + -1
0.8571428571n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.8571428571n + n2 = -1

The n term is 0.8571428571n.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571n + 0.1836734694 + n2 = -1 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571n + n2 = -1 + 0.1836734694

Combine like terms: -1 + 0.1836734694 = -0.8163265306
0.1836734694 + 0.8571428571n + n2 = -0.8163265306

Factor a perfect square on the left side:
(n + 0.4285714286)(n + 0.4285714286) = -0.8163265306

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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