n^2+n-100=0

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Solution for n^2+n-100=0 equation:


Simplifying
n2 + n + -100 = 0

Reorder the terms:
-100 + n + n2 = 0

Solving
-100 + n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + n + 100 + n2 = 0 + 100

Reorder the terms:
-100 + 100 + n + n2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + n + n2 = 0 + 100
n + n2 = 0 + 100

Combine like terms: 0 + 100 = 100
n + n2 = 100

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = 100 + 0.25

Reorder the terms:
0.25 + n + n2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
0.25 + n + n2 = 100.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(n + 0.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

n + 0.5 = 10.012492197 Simplifying n + 0.5 = 10.012492197 Reorder the terms: 0.5 + n = 10.012492197 Solving 0.5 + n = 10.012492197 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 10.012492197 + -0.5 n = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 n = 9.512492197 Simplifying n = 9.512492197

Subproblem 2

n + 0.5 = -10.012492197 Simplifying n + 0.5 = -10.012492197 Reorder the terms: 0.5 + n = -10.012492197 Solving 0.5 + n = -10.012492197 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -10.012492197 + -0.5 n = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 n = -10.512492197 Simplifying n = -10.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. n = {9.512492197, -10.512492197}

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