n^2+4n-69=0

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Solution for n^2+4n-69=0 equation:


Simplifying
n2 + 4n + -69 = 0

Reorder the terms:
-69 + 4n + n2 = 0

Solving
-69 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '69' to each side of the equation.
-69 + 4n + 69 + n2 = 0 + 69

Reorder the terms:
-69 + 69 + 4n + n2 = 0 + 69

Combine like terms: -69 + 69 = 0
0 + 4n + n2 = 0 + 69
4n + n2 = 0 + 69

Combine like terms: 0 + 69 = 69
4n + n2 = 69

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 = 69 + 4

Reorder the terms:
4 + 4n + n2 = 69 + 4

Combine like terms: 69 + 4 = 73
4 + 4n + n2 = 73

Factor a perfect square on the left side:
(n + 2)(n + 2) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(n + 2) equal to 8.544003745 and -8.544003745.

Subproblem 1

n + 2 = 8.544003745 Simplifying n + 2 = 8.544003745 Reorder the terms: 2 + n = 8.544003745 Solving 2 + n = 8.544003745 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 = 8.544003745 + -2 Combine like terms: 2 + -2 = 0 0 + n = 8.544003745 + -2 n = 8.544003745 + -2 Combine like terms: 8.544003745 + -2 = 6.544003745 n = 6.544003745 Simplifying n = 6.544003745

Subproblem 2

n + 2 = -8.544003745 Simplifying n + 2 = -8.544003745 Reorder the terms: 2 + n = -8.544003745 Solving 2 + n = -8.544003745 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 = -8.544003745 + -2 Combine like terms: 2 + -2 = 0 0 + n = -8.544003745 + -2 n = -8.544003745 + -2 Combine like terms: -8.544003745 + -2 = -10.544003745 n = -10.544003745 Simplifying n = -10.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.544003745, -10.544003745}

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