5n^2+8n-20=0

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Solution for 5n^2+8n-20=0 equation:


Simplifying
5n2 + 8n + -20 = 0

Reorder the terms:
-20 + 8n + 5n2 = 0

Solving
-20 + 8n + 5n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-4 + 1.6n + n2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.6n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.6n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.6n + n2 = 0 + 4
1.6n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.6n + n2 = 4

The n term is 1.6n.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6n + 0.64 + n2 = 4 + 0.64

Reorder the terms:
0.64 + 1.6n + n2 = 4 + 0.64

Combine like terms: 4 + 0.64 = 4.64
0.64 + 1.6n + n2 = 4.64

Factor a perfect square on the left side:
(n + 0.8)(n + 0.8) = 4.64

Calculate the square root of the right side: 2.154065923

Break this problem into two subproblems by setting 
(n + 0.8) equal to 2.154065923 and -2.154065923.

Subproblem 1

n + 0.8 = 2.154065923 Simplifying n + 0.8 = 2.154065923 Reorder the terms: 0.8 + n = 2.154065923 Solving 0.8 + n = 2.154065923 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + n = 2.154065923 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + n = 2.154065923 + -0.8 n = 2.154065923 + -0.8 Combine like terms: 2.154065923 + -0.8 = 1.354065923 n = 1.354065923 Simplifying n = 1.354065923

Subproblem 2

n + 0.8 = -2.154065923 Simplifying n + 0.8 = -2.154065923 Reorder the terms: 0.8 + n = -2.154065923 Solving 0.8 + n = -2.154065923 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + n = -2.154065923 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + n = -2.154065923 + -0.8 n = -2.154065923 + -0.8 Combine like terms: -2.154065923 + -0.8 = -2.954065923 n = -2.954065923 Simplifying n = -2.954065923

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.354065923, -2.954065923}

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