9n^2+10n-8=0

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Solution for 9n^2+10n-8=0 equation:


Simplifying
9n2 + 10n + -8 = 0

Reorder the terms:
-8 + 10n + 9n2 = 0

Solving
-8 + 10n + 9n2 = 0

Solving for variable 'n'.

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

Divide each side by '9'.
-0.8888888889 + 1.111111111n + n2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 1.111111111n + 0.8888888889 + n2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 1.111111111n + n2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 1.111111111n + n2 = 0 + 0.8888888889
1.111111111n + n2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
1.111111111n + n2 = 0.8888888889

The n term is 1.111111111n.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111n + 0.3086419752 + n2 = 0.8888888889 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111n + n2 = 0.8888888889 + 0.3086419752

Combine like terms: 0.8888888889 + 0.3086419752 = 1.1975308641
0.3086419752 + 1.111111111n + n2 = 1.1975308641

Factor a perfect square on the left side:
(n + 0.5555555555)(n + 0.5555555555) = 1.1975308641

Calculate the square root of the right side: 1.094317533

Break this problem into two subproblems by setting 
(n + 0.5555555555) equal to 1.094317533 and -1.094317533.

Subproblem 1

n + 0.5555555555 = 1.094317533 Simplifying n + 0.5555555555 = 1.094317533 Reorder the terms: 0.5555555555 + n = 1.094317533 Solving 0.5555555555 + n = 1.094317533 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + n = 1.094317533 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + n = 1.094317533 + -0.5555555555 n = 1.094317533 + -0.5555555555 Combine like terms: 1.094317533 + -0.5555555555 = 0.5387619775 n = 0.5387619775 Simplifying n = 0.5387619775

Subproblem 2

n + 0.5555555555 = -1.094317533 Simplifying n + 0.5555555555 = -1.094317533 Reorder the terms: 0.5555555555 + n = -1.094317533 Solving 0.5555555555 + n = -1.094317533 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + n = -1.094317533 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + n = -1.094317533 + -0.5555555555 n = -1.094317533 + -0.5555555555 Combine like terms: -1.094317533 + -0.5555555555 = -1.6498730885 n = -1.6498730885 Simplifying n = -1.6498730885

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.5387619775, -1.6498730885}

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