7n^2+134=6n^2+13n+10

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Solution for 7n^2+134=6n^2+13n+10 equation: 


Simplifying
7n2 + 134 = 6n2 + 13n + 10

Reorder the terms:
134 + 7n2 = 6n2 + 13n + 10

Reorder the terms:
134 + 7n2 = 10 + 13n + 6n2

Solving
134 + 7n2 = 10 + 13n + 6n2

Solving for variable 'n'.

Reorder the terms:
134 + -10 + -13n + 7n2 + -6n2 = 10 + 13n + 6n2 + -10 + -13n + -6n2

Combine like terms: 134 + -10 = 124
124 + -13n + 7n2 + -6n2 = 10 + 13n + 6n2 + -10 + -13n + -6n2

Combine like terms: 7n2 + -6n2 = 1n2
124 + -13n + 1n2 = 10 + 13n + 6n2 + -10 + -13n + -6n2

Reorder the terms:
124 + -13n + 1n2 = 10 + -10 + 13n + -13n + 6n2 + -6n2

Combine like terms: 10 + -10 = 0
124 + -13n + 1n2 = 0 + 13n + -13n + 6n2 + -6n2
124 + -13n + 1n2 = 13n + -13n + 6n2 + -6n2

Combine like terms: 13n + -13n = 0
124 + -13n + 1n2 = 0 + 6n2 + -6n2
124 + -13n + 1n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
124 + -13n + 1n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-124' to each side of the equation.
124 + -13n + -124 + n2 = 0 + -124

Reorder the terms:
124 + -124 + -13n + n2 = 0 + -124

Combine like terms: 124 + -124 = 0
0 + -13n + n2 = 0 + -124
-13n + n2 = 0 + -124

Combine like terms: 0 + -124 = -124
-13n + n2 = -124

The n term is -13n.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13n + 42.25 + n2 = -124 + 42.25

Reorder the terms:
42.25 + -13n + n2 = -124 + 42.25

Combine like terms: -124 + 42.25 = -81.75
42.25 + -13n + n2 = -81.75

Factor a perfect square on the left side:
(n + -6.5)(n + -6.5) = -81.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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