n^2-14n+49=6

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Solution for n^2-14n+49=6 equation:


Simplifying
n2 + -14n + 49 = 6

Reorder the terms:
49 + -14n + n2 = 6

Solving
49 + -14n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
49 + -6 + -14n + n2 = 6 + -6

Combine like terms: 49 + -6 = 43
43 + -14n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
43 + -14n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + -14n + -43 + n2 = 0 + -43

Reorder the terms:
43 + -43 + -14n + n2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -14n + n2 = 0 + -43
-14n + n2 = 0 + -43

Combine like terms: 0 + -43 = -43
-14n + n2 = -43

The n term is -14n.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14n + 49 + n2 = -43 + 49

Reorder the terms:
49 + -14n + n2 = -43 + 49

Combine like terms: -43 + 49 = 6
49 + -14n + n2 = 6

Factor a perfect square on the left side:
(n + -7)(n + -7) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(n + -7) equal to 2.449489743 and -2.449489743.

Subproblem 1

n + -7 = 2.449489743 Simplifying n + -7 = 2.449489743 Reorder the terms: -7 + n = 2.449489743 Solving -7 + n = 2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + n = 2.449489743 + 7 n = 2.449489743 + 7 Combine like terms: 2.449489743 + 7 = 9.449489743 n = 9.449489743 Simplifying n = 9.449489743

Subproblem 2

n + -7 = -2.449489743 Simplifying n + -7 = -2.449489743 Reorder the terms: -7 + n = -2.449489743 Solving -7 + n = -2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + n = -2.449489743 + 7 n = -2.449489743 + 7 Combine like terms: -2.449489743 + 7 = 4.550510257 n = 4.550510257 Simplifying n = 4.550510257

Solution

The solution to the problem is based on the solutions from the subproblems. n = {9.449489743, 4.550510257}

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