n^2-9n-16=0

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Solution for n^2-9n-16=0 equation:


Simplifying
n2 + -9n + -16 = 0

Reorder the terms:
-16 + -9n + n2 = 0

Solving
-16 + -9n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -9n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + -9n + n2 = 0 + 16

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

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

The n term is -9n.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9n + 20.25 + n2 = 16 + 20.25

Reorder the terms:
20.25 + -9n + n2 = 16 + 20.25

Combine like terms: 16 + 20.25 = 36.25
20.25 + -9n + n2 = 36.25

Factor a perfect square on the left side:
(n + -4.5)(n + -4.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(n + -4.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

n + -4.5 = 6.020797289 Simplifying n + -4.5 = 6.020797289 Reorder the terms: -4.5 + n = 6.020797289 Solving -4.5 + n = 6.020797289 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 6.020797289 + 4.5 n = 6.020797289 + 4.5 Combine like terms: 6.020797289 + 4.5 = 10.520797289 n = 10.520797289 Simplifying n = 10.520797289

Subproblem 2

n + -4.5 = -6.020797289 Simplifying n + -4.5 = -6.020797289 Reorder the terms: -4.5 + n = -6.020797289 Solving -4.5 + n = -6.020797289 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -6.020797289 + 4.5 n = -6.020797289 + 4.5 Combine like terms: -6.020797289 + 4.5 = -1.520797289 n = -1.520797289 Simplifying n = -1.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.520797289, -1.520797289}

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