5n^2-8n+2=0

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


Simplifying
5n2 + -8n + 2 = 0

Reorder the terms:
2 + -8n + 5n2 = 0

Solving
2 + -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'.
0.4 + -1.6n + n2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -1.6n + -0.4 + n2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -1.6n + n2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -1.6n + n2 = 0 + -0.4
-1.6n + n2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-1.6n + n2 = -0.4

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 = -0.4 + 0.64

Reorder the terms:
0.64 + -1.6n + n2 = -0.4 + 0.64

Combine like terms: -0.4 + 0.64 = 0.24
0.64 + -1.6n + n2 = 0.24

Factor a perfect square on the left side:
(n + -0.8)(n + -0.8) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(n + -0.8) equal to 0.489897949 and -0.489897949.

Subproblem 1

n + -0.8 = 0.489897949 Simplifying n + -0.8 = 0.489897949 Reorder the terms: -0.8 + n = 0.489897949 Solving -0.8 + n = 0.489897949 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 = 0.489897949 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = 0.489897949 + 0.8 n = 0.489897949 + 0.8 Combine like terms: 0.489897949 + 0.8 = 1.289897949 n = 1.289897949 Simplifying n = 1.289897949

Subproblem 2

n + -0.8 = -0.489897949 Simplifying n + -0.8 = -0.489897949 Reorder the terms: -0.8 + n = -0.489897949 Solving -0.8 + n = -0.489897949 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 = -0.489897949 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = -0.489897949 + 0.8 n = -0.489897949 + 0.8 Combine like terms: -0.489897949 + 0.8 = 0.310102051 n = 0.310102051 Simplifying n = 0.310102051

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.289897949, 0.310102051}

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