n^2+4n=40

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Solution for n^2+4n=40 equation:


Simplifying
n2 + 4n = 40

Reorder the terms:
4n + n2 = 40

Solving
4n + n2 = 40

Solving for variable 'n'.

Reorder the terms:
-40 + 4n + n2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 4n + 40 + n2 = 0 + 40

Reorder the terms:
-40 + 40 + 4n + n2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 4n + n2 = 0 + 40
4n + n2 = 0 + 40

Combine like terms: 0 + 40 = 40
4n + n2 = 40

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 = 40 + 4

Reorder the terms:
4 + 4n + n2 = 40 + 4

Combine like terms: 40 + 4 = 44
4 + 4n + n2 = 44

Factor a perfect square on the left side:
(n + 2)(n + 2) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(n + 2) equal to 6.633249581 and -6.633249581.

Subproblem 1

n + 2 = 6.633249581 Simplifying n + 2 = 6.633249581 Reorder the terms: 2 + n = 6.633249581 Solving 2 + n = 6.633249581 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 = 6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + n = 6.633249581 + -2 n = 6.633249581 + -2 Combine like terms: 6.633249581 + -2 = 4.633249581 n = 4.633249581 Simplifying n = 4.633249581

Subproblem 2

n + 2 = -6.633249581 Simplifying n + 2 = -6.633249581 Reorder the terms: 2 + n = -6.633249581 Solving 2 + n = -6.633249581 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 = -6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + n = -6.633249581 + -2 n = -6.633249581 + -2 Combine like terms: -6.633249581 + -2 = -8.633249581 n = -8.633249581 Simplifying n = -8.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. n = {4.633249581, -8.633249581}

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