n^2+4n=9

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Solution for n^2+4n=9 equation:


Simplifying
n2 + 4n = 9

Reorder the terms:
4n + n2 = 9

Solving
4n + n2 = 9

Solving for variable 'n'.

Reorder the terms:
-9 + 4n + n2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 4n + 9 + n2 = 0 + 9

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

Combine like terms: -9 + 9 = 0
0 + 4n + n2 = 0 + 9
4n + n2 = 0 + 9

Combine like terms: 0 + 9 = 9
4n + n2 = 9

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 9 + 4

Reorder the terms:
4 + 4n + n2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + 4n + n2 = 13

Factor a perfect square on the left side:
(n + 2)(n + 2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(n + 2) equal to 3.605551275 and -3.605551275.

Subproblem 1

n + 2 = 3.605551275 Simplifying n + 2 = 3.605551275 Reorder the terms: 2 + n = 3.605551275 Solving 2 + n = 3.605551275 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + n = 3.605551275 + -2 n = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 n = 1.605551275 Simplifying n = 1.605551275

Subproblem 2

n + 2 = -3.605551275 Simplifying n + 2 = -3.605551275 Reorder the terms: 2 + n = -3.605551275 Solving 2 + n = -3.605551275 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + n = -3.605551275 + -2 n = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 n = -5.605551275 Simplifying n = -5.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.605551275, -5.605551275}

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