n^2+20n-52=0

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Solution for n^2+20n-52=0 equation:


Simplifying
n2 + 20n + -52 = 0

Reorder the terms:
-52 + 20n + n2 = 0

Solving
-52 + 20n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 20n + 52 + n2 = 0 + 52

Reorder the terms:
-52 + 52 + 20n + n2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 20n + n2 = 0 + 52
20n + n2 = 0 + 52

Combine like terms: 0 + 52 = 52
20n + n2 = 52

The n term is 20n.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20n + 100 + n2 = 52 + 100

Reorder the terms:
100 + 20n + n2 = 52 + 100

Combine like terms: 52 + 100 = 152
100 + 20n + n2 = 152

Factor a perfect square on the left side:
(n + 10)(n + 10) = 152

Calculate the square root of the right side: 12.328828006

Break this problem into two subproblems by setting 
(n + 10) equal to 12.328828006 and -12.328828006.

Subproblem 1

n + 10 = 12.328828006 Simplifying n + 10 = 12.328828006 Reorder the terms: 10 + n = 12.328828006 Solving 10 + n = 12.328828006 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 12.328828006 + -10 Combine like terms: 10 + -10 = 0 0 + n = 12.328828006 + -10 n = 12.328828006 + -10 Combine like terms: 12.328828006 + -10 = 2.328828006 n = 2.328828006 Simplifying n = 2.328828006

Subproblem 2

n + 10 = -12.328828006 Simplifying n + 10 = -12.328828006 Reorder the terms: 10 + n = -12.328828006 Solving 10 + n = -12.328828006 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = -12.328828006 + -10 Combine like terms: 10 + -10 = 0 0 + n = -12.328828006 + -10 n = -12.328828006 + -10 Combine like terms: -12.328828006 + -10 = -22.328828006 n = -22.328828006 Simplifying n = -22.328828006

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.328828006, -22.328828006}

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