n^2+8n-400=0

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Solution for n^2+8n-400=0 equation:


Simplifying
n2 + 8n + -400 = 0

Reorder the terms:
-400 + 8n + n2 = 0

Solving
-400 + 8n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 8n + 400 + n2 = 0 + 400

Reorder the terms:
-400 + 400 + 8n + n2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 8n + n2 = 0 + 400
8n + n2 = 0 + 400

Combine like terms: 0 + 400 = 400
8n + n2 = 400

The n term is 8n.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8n + 16 + n2 = 400 + 16

Reorder the terms:
16 + 8n + n2 = 400 + 16

Combine like terms: 400 + 16 = 416
16 + 8n + n2 = 416

Factor a perfect square on the left side:
(n + 4)(n + 4) = 416

Calculate the square root of the right side: 20.396078054

Break this problem into two subproblems by setting 
(n + 4) equal to 20.396078054 and -20.396078054.

Subproblem 1

n + 4 = 20.396078054 Simplifying n + 4 = 20.396078054 Reorder the terms: 4 + n = 20.396078054 Solving 4 + n = 20.396078054 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 20.396078054 + -4 Combine like terms: 4 + -4 = 0 0 + n = 20.396078054 + -4 n = 20.396078054 + -4 Combine like terms: 20.396078054 + -4 = 16.396078054 n = 16.396078054 Simplifying n = 16.396078054

Subproblem 2

n + 4 = -20.396078054 Simplifying n + 4 = -20.396078054 Reorder the terms: 4 + n = -20.396078054 Solving 4 + n = -20.396078054 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -20.396078054 + -4 Combine like terms: 4 + -4 = 0 0 + n = -20.396078054 + -4 n = -20.396078054 + -4 Combine like terms: -20.396078054 + -4 = -24.396078054 n = -24.396078054 Simplifying n = -24.396078054

Solution

The solution to the problem is based on the solutions from the subproblems. n = {16.396078054, -24.396078054}

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