n^2-7n+2=0

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Solution for n^2-7n+2=0 equation:


Simplifying
n2 + -7n + 2 = 0

Reorder the terms:
2 + -7n + n2 = 0

Solving
2 + -7n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + -7n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7n + n2 = 0 + -2
-7n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7n + n2 = -2

The n term is -7n.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7n + 12.25 + n2 = -2 + 12.25

Reorder the terms:
12.25 + -7n + n2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + -7n + n2 = 10.25

Factor a perfect square on the left side:
(n + -3.5)(n + -3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(n + -3.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

n + -3.5 = 3.201562119 Simplifying n + -3.5 = 3.201562119 Reorder the terms: -3.5 + n = 3.201562119 Solving -3.5 + n = 3.201562119 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = 3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = 3.201562119 + 3.5 n = 3.201562119 + 3.5 Combine like terms: 3.201562119 + 3.5 = 6.701562119 n = 6.701562119 Simplifying n = 6.701562119

Subproblem 2

n + -3.5 = -3.201562119 Simplifying n + -3.5 = -3.201562119 Reorder the terms: -3.5 + n = -3.201562119 Solving -3.5 + n = -3.201562119 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = -3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = -3.201562119 + 3.5 n = -3.201562119 + 3.5 Combine like terms: -3.201562119 + 3.5 = 0.298437881 n = 0.298437881 Simplifying n = 0.298437881

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.701562119, 0.298437881}

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