n^2-14n-22=0

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Solution for n^2-14n-22=0 equation:


Simplifying
n2 + -14n + -22 = 0

Reorder the terms:
-22 + -14n + n2 = 0

Solving
-22 + -14n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -14n + 22 + n2 = 0 + 22

Reorder the terms:
-22 + 22 + -14n + n2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -14n + n2 = 0 + 22
-14n + n2 = 0 + 22

Combine like terms: 0 + 22 = 22
-14n + n2 = 22

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 = 22 + 49

Reorder the terms:
49 + -14n + n2 = 22 + 49

Combine like terms: 22 + 49 = 71
49 + -14n + n2 = 71

Factor a perfect square on the left side:
(n + -7)(n + -7) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(n + -7) equal to 8.426149773 and -8.426149773.

Subproblem 1

n + -7 = 8.426149773 Simplifying n + -7 = 8.426149773 Reorder the terms: -7 + n = 8.426149773 Solving -7 + n = 8.426149773 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 = 8.426149773 + 7 Combine like terms: -7 + 7 = 0 0 + n = 8.426149773 + 7 n = 8.426149773 + 7 Combine like terms: 8.426149773 + 7 = 15.426149773 n = 15.426149773 Simplifying n = 15.426149773

Subproblem 2

n + -7 = -8.426149773 Simplifying n + -7 = -8.426149773 Reorder the terms: -7 + n = -8.426149773 Solving -7 + n = -8.426149773 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 = -8.426149773 + 7 Combine like terms: -7 + 7 = 0 0 + n = -8.426149773 + 7 n = -8.426149773 + 7 Combine like terms: -8.426149773 + 7 = -1.426149773 n = -1.426149773 Simplifying n = -1.426149773

Solution

The solution to the problem is based on the solutions from the subproblems. n = {15.426149773, -1.426149773}

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