(9n^2+6n)-(-7n^2-4n+5)=

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Solution for (9n^2+6n)-(-7n^2-4n+5)= equation:


Simplifying
(9n2 + 6n) + -1(-7n2 + -4n + 5) = 0

Reorder the terms:
(6n + 9n2) + -1(-7n2 + -4n + 5) = 0

Remove parenthesis around (6n + 9n2)
6n + 9n2 + -1(-7n2 + -4n + 5) = 0

Reorder the terms:
6n + 9n2 + -1(5 + -4n + -7n2) = 0
6n + 9n2 + (5 * -1 + -4n * -1 + -7n2 * -1) = 0
6n + 9n2 + (-5 + 4n + 7n2) = 0

Reorder the terms:
-5 + 6n + 4n + 9n2 + 7n2 = 0

Combine like terms: 6n + 4n = 10n
-5 + 10n + 9n2 + 7n2 = 0

Combine like terms: 9n2 + 7n2 = 16n2
-5 + 10n + 16n2 = 0

Solving
-5 + 10n + 16n2 = 0

Solving for variable 'n'.

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

Divide each side by '16'.
-0.3125 + 0.625n + n2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + 0.625n + 0.3125 + n2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + 0.625n + n2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + 0.625n + n2 = 0 + 0.3125
0.625n + n2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
0.625n + n2 = 0.3125

The n term is 0.625n.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625n + 0.09765625 + n2 = 0.3125 + 0.09765625

Reorder the terms:
0.09765625 + 0.625n + n2 = 0.3125 + 0.09765625

Combine like terms: 0.3125 + 0.09765625 = 0.41015625
0.09765625 + 0.625n + n2 = 0.41015625

Factor a perfect square on the left side:
(n + 0.3125)(n + 0.3125) = 0.41015625

Calculate the square root of the right side: 0.640434423

Break this problem into two subproblems by setting 
(n + 0.3125) equal to 0.640434423 and -0.640434423.

Subproblem 1

n + 0.3125 = 0.640434423 Simplifying n + 0.3125 = 0.640434423 Reorder the terms: 0.3125 + n = 0.640434423 Solving 0.3125 + n = 0.640434423 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + n = 0.640434423 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + n = 0.640434423 + -0.3125 n = 0.640434423 + -0.3125 Combine like terms: 0.640434423 + -0.3125 = 0.327934423 n = 0.327934423 Simplifying n = 0.327934423

Subproblem 2

n + 0.3125 = -0.640434423 Simplifying n + 0.3125 = -0.640434423 Reorder the terms: 0.3125 + n = -0.640434423 Solving 0.3125 + n = -0.640434423 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + n = -0.640434423 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + n = -0.640434423 + -0.3125 n = -0.640434423 + -0.3125 Combine like terms: -0.640434423 + -0.3125 = -0.952934423 n = -0.952934423 Simplifying n = -0.952934423

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.327934423, -0.952934423}

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