2n^2-9n-9=0

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Solution for 2n^2-9n-9=0 equation:


Simplifying
2n2 + -9n + -9 = 0

Reorder the terms:
-9 + -9n + 2n2 = 0

Solving
-9 + -9n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
-4.5 + -4.5n + n2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -4.5n + 4.5 + n2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -4.5n + n2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -4.5n + n2 = 0 + 4.5
-4.5n + n2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-4.5n + n2 = 4.5

The n term is -4.5n.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5n + 5.0625 + n2 = 4.5 + 5.0625

Reorder the terms:
5.0625 + -4.5n + n2 = 4.5 + 5.0625

Combine like terms: 4.5 + 5.0625 = 9.5625
5.0625 + -4.5n + n2 = 9.5625

Factor a perfect square on the left side:
(n + -2.25)(n + -2.25) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(n + -2.25) equal to 3.092329219 and -3.092329219.

Subproblem 1

n + -2.25 = 3.092329219 Simplifying n + -2.25 = 3.092329219 Reorder the terms: -2.25 + n = 3.092329219 Solving -2.25 + n = 3.092329219 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + n = 3.092329219 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + n = 3.092329219 + 2.25 n = 3.092329219 + 2.25 Combine like terms: 3.092329219 + 2.25 = 5.342329219 n = 5.342329219 Simplifying n = 5.342329219

Subproblem 2

n + -2.25 = -3.092329219 Simplifying n + -2.25 = -3.092329219 Reorder the terms: -2.25 + n = -3.092329219 Solving -2.25 + n = -3.092329219 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + n = -3.092329219 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + n = -3.092329219 + 2.25 n = -3.092329219 + 2.25 Combine like terms: -3.092329219 + 2.25 = -0.842329219 n = -0.842329219 Simplifying n = -0.842329219

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.342329219, -0.842329219}

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