n*(n-3)=66

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Solution for n*(n-3)=66 equation:


Simplifying
n(n + -3) = 66

Reorder the terms:
n(-3 + n) = 66
(-3 * n + n * n) = 66
(-3n + n2) = 66

Solving
-3n + n2 = 66

Solving for variable 'n'.

Reorder the terms:
-66 + -3n + n2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + -3n + 66 + n2 = 0 + 66

Reorder the terms:
-66 + 66 + -3n + n2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + -3n + n2 = 0 + 66
-3n + n2 = 0 + 66

Combine like terms: 0 + 66 = 66
-3n + n2 = 66

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 66 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 66 + 2.25

Combine like terms: 66 + 2.25 = 68.25
2.25 + -3n + n2 = 68.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(n + -1.5) equal to 8.261355821 and -8.261355821.

Subproblem 1

n + -1.5 = 8.261355821 Simplifying n + -1.5 = 8.261355821 Reorder the terms: -1.5 + n = 8.261355821 Solving -1.5 + n = 8.261355821 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 8.261355821 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 8.261355821 + 1.5 n = 8.261355821 + 1.5 Combine like terms: 8.261355821 + 1.5 = 9.761355821 n = 9.761355821 Simplifying n = 9.761355821

Subproblem 2

n + -1.5 = -8.261355821 Simplifying n + -1.5 = -8.261355821 Reorder the terms: -1.5 + n = -8.261355821 Solving -1.5 + n = -8.261355821 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -8.261355821 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -8.261355821 + 1.5 n = -8.261355821 + 1.5 Combine like terms: -8.261355821 + 1.5 = -6.761355821 n = -6.761355821 Simplifying n = -6.761355821

Solution

The solution to the problem is based on the solutions from the subproblems. n = {9.761355821, -6.761355821}

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