n^2-n-48=0

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Solution for n^2-n-48=0 equation:


Simplifying
n2 + -1n + -48 = 0

Reorder the terms:
-48 + -1n + n2 = 0

Solving
-48 + -1n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -1n + 48 + n2 = 0 + 48

Reorder the terms:
-48 + 48 + -1n + n2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -1n + n2 = 0 + 48
-1n + n2 = 0 + 48

Combine like terms: 0 + 48 = 48
-1n + n2 = 48

The n term is -1n.  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.
-1n + 0.25 + n2 = 48 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 48 + 0.25

Combine like terms: 48 + 0.25 = 48.25
0.25 + -1n + n2 = 48.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(n + -0.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

n + -0.5 = 6.946221995 Simplifying n + -0.5 = 6.946221995 Reorder the terms: -0.5 + n = 6.946221995 Solving -0.5 + n = 6.946221995 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 = 6.946221995 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 6.946221995 + 0.5 n = 6.946221995 + 0.5 Combine like terms: 6.946221995 + 0.5 = 7.446221995 n = 7.446221995 Simplifying n = 7.446221995

Subproblem 2

n + -0.5 = -6.946221995 Simplifying n + -0.5 = -6.946221995 Reorder the terms: -0.5 + n = -6.946221995 Solving -0.5 + n = -6.946221995 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 = -6.946221995 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -6.946221995 + 0.5 n = -6.946221995 + 0.5 Combine like terms: -6.946221995 + 0.5 = -6.446221995 n = -6.446221995 Simplifying n = -6.446221995

Solution

The solution to the problem is based on the solutions from the subproblems. n = {7.446221995, -6.446221995}

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