2n^2-7n-3=0

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Solution for 2n^2-7n-3=0 equation:


Simplifying
2n2 + -7n + -3 = 0

Reorder the terms:
-3 + -7n + 2n2 = 0

Solving
-3 + -7n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
-1.5 + -3.5n + n2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -3.5n + 1.5 + n2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -3.5n + n2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -3.5n + n2 = 0 + 1.5
-3.5n + n2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-3.5n + n2 = 1.5

The n term is -3.5n.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5n + 3.0625 + n2 = 1.5 + 3.0625

Reorder the terms:
3.0625 + -3.5n + n2 = 1.5 + 3.0625

Combine like terms: 1.5 + 3.0625 = 4.5625
3.0625 + -3.5n + n2 = 4.5625

Factor a perfect square on the left side:
(n + -1.75)(n + -1.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(n + -1.75) equal to 2.136000936 and -2.136000936.

Subproblem 1

n + -1.75 = 2.136000936 Simplifying n + -1.75 = 2.136000936 Reorder the terms: -1.75 + n = 2.136000936 Solving -1.75 + n = 2.136000936 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + n = 2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = 2.136000936 + 1.75 n = 2.136000936 + 1.75 Combine like terms: 2.136000936 + 1.75 = 3.886000936 n = 3.886000936 Simplifying n = 3.886000936

Subproblem 2

n + -1.75 = -2.136000936 Simplifying n + -1.75 = -2.136000936 Reorder the terms: -1.75 + n = -2.136000936 Solving -1.75 + n = -2.136000936 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + n = -2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = -2.136000936 + 1.75 n = -2.136000936 + 1.75 Combine like terms: -2.136000936 + 1.75 = -0.386000936 n = -0.386000936 Simplifying n = -0.386000936

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.886000936, -0.386000936}

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