5n^2+20n-68=-2

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Solution for 5n^2+20n-68=-2 equation:


Simplifying
5n2 + 20n + -68 = -2

Reorder the terms:
-68 + 20n + 5n2 = -2

Solving
-68 + 20n + 5n2 = -2

Solving for variable 'n'.

Reorder the terms:
-68 + 2 + 20n + 5n2 = -2 + 2

Combine like terms: -68 + 2 = -66
-66 + 20n + 5n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-66 + 20n + 5n2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-13.2 + 4n + n2 = 0

Move the constant term to the right:

Add '13.2' to each side of the equation.
-13.2 + 4n + 13.2 + n2 = 0 + 13.2

Reorder the terms:
-13.2 + 13.2 + 4n + n2 = 0 + 13.2

Combine like terms: -13.2 + 13.2 = 0.0
0.0 + 4n + n2 = 0 + 13.2
4n + n2 = 0 + 13.2

Combine like terms: 0 + 13.2 = 13.2
4n + n2 = 13.2

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 13.2 + 4

Reorder the terms:
4 + 4n + n2 = 13.2 + 4

Combine like terms: 13.2 + 4 = 17.2
4 + 4n + n2 = 17.2

Factor a perfect square on the left side:
(n + 2)(n + 2) = 17.2

Calculate the square root of the right side: 4.147288271

Break this problem into two subproblems by setting 
(n + 2) equal to 4.147288271 and -4.147288271.

Subproblem 1

n + 2 = 4.147288271 Simplifying n + 2 = 4.147288271 Reorder the terms: 2 + n = 4.147288271 Solving 2 + n = 4.147288271 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 4.147288271 + -2 Combine like terms: 2 + -2 = 0 0 + n = 4.147288271 + -2 n = 4.147288271 + -2 Combine like terms: 4.147288271 + -2 = 2.147288271 n = 2.147288271 Simplifying n = 2.147288271

Subproblem 2

n + 2 = -4.147288271 Simplifying n + 2 = -4.147288271 Reorder the terms: 2 + n = -4.147288271 Solving 2 + n = -4.147288271 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -4.147288271 + -2 Combine like terms: 2 + -2 = 0 0 + n = -4.147288271 + -2 n = -4.147288271 + -2 Combine like terms: -4.147288271 + -2 = -6.147288271 n = -6.147288271 Simplifying n = -6.147288271

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.147288271, -6.147288271}

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