n^2-2n-35=14

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Solution for n^2-2n-35=14 equation:


Simplifying
n2 + -2n + -35 = 14

Reorder the terms:
-35 + -2n + n2 = 14

Solving
-35 + -2n + n2 = 14

Solving for variable 'n'.

Reorder the terms:
-35 + -14 + -2n + n2 = 14 + -14

Combine like terms: -35 + -14 = -49
-49 + -2n + n2 = 14 + -14

Combine like terms: 14 + -14 = 0
-49 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -2n + 49 + n2 = 0 + 49

Reorder the terms:
-49 + 49 + -2n + n2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -2n + n2 = 0 + 49
-2n + n2 = 0 + 49

Combine like terms: 0 + 49 = 49
-2n + n2 = 49

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 49 + 1

Reorder the terms:
1 + -2n + n2 = 49 + 1

Combine like terms: 49 + 1 = 50
1 + -2n + n2 = 50

Factor a perfect square on the left side:
(n + -1)(n + -1) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(n + -1) equal to 7.071067812 and -7.071067812.

Subproblem 1

n + -1 = 7.071067812 Simplifying n + -1 = 7.071067812 Reorder the terms: -1 + n = 7.071067812 Solving -1 + n = 7.071067812 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 7.071067812 + 1 Combine like terms: -1 + 1 = 0 0 + n = 7.071067812 + 1 n = 7.071067812 + 1 Combine like terms: 7.071067812 + 1 = 8.071067812 n = 8.071067812 Simplifying n = 8.071067812

Subproblem 2

n + -1 = -7.071067812 Simplifying n + -1 = -7.071067812 Reorder the terms: -1 + n = -7.071067812 Solving -1 + n = -7.071067812 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -7.071067812 + 1 Combine like terms: -1 + 1 = 0 0 + n = -7.071067812 + 1 n = -7.071067812 + 1 Combine like terms: -7.071067812 + 1 = -6.071067812 n = -6.071067812 Simplifying n = -6.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. n = {8.071067812, -6.071067812}

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