n^2+5n=288

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Solution for n^2+5n=288 equation:


Simplifying
n2 + 5n = 288

Reorder the terms:
5n + n2 = 288

Solving
5n + n2 = 288

Solving for variable 'n'.

Reorder the terms:
-288 + 5n + n2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '288' to each side of the equation.
-288 + 5n + 288 + n2 = 0 + 288

Reorder the terms:
-288 + 288 + 5n + n2 = 0 + 288

Combine like terms: -288 + 288 = 0
0 + 5n + n2 = 0 + 288
5n + n2 = 0 + 288

Combine like terms: 0 + 288 = 288
5n + n2 = 288

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = 288 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 288 + 6.25

Combine like terms: 288 + 6.25 = 294.25
6.25 + 5n + n2 = 294.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 294.25

Calculate the square root of the right side: 17.153716798

Break this problem into two subproblems by setting 
(n + 2.5) equal to 17.153716798 and -17.153716798.

Subproblem 1

n + 2.5 = 17.153716798 Simplifying n + 2.5 = 17.153716798 Reorder the terms: 2.5 + n = 17.153716798 Solving 2.5 + n = 17.153716798 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 17.153716798 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 17.153716798 + -2.5 n = 17.153716798 + -2.5 Combine like terms: 17.153716798 + -2.5 = 14.653716798 n = 14.653716798 Simplifying n = 14.653716798

Subproblem 2

n + 2.5 = -17.153716798 Simplifying n + 2.5 = -17.153716798 Reorder the terms: 2.5 + n = -17.153716798 Solving 2.5 + n = -17.153716798 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -17.153716798 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -17.153716798 + -2.5 n = -17.153716798 + -2.5 Combine like terms: -17.153716798 + -2.5 = -19.653716798 n = -19.653716798 Simplifying n = -19.653716798

Solution

The solution to the problem is based on the solutions from the subproblems. n = {14.653716798, -19.653716798}

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