2n^2+8n-67=-10

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Solution for 2n^2+8n-67=-10 equation:


Simplifying
2n2 + 8n + -67 = -10

Reorder the terms:
-67 + 8n + 2n2 = -10

Solving
-67 + 8n + 2n2 = -10

Solving for variable 'n'.

Reorder the terms:
-67 + 10 + 8n + 2n2 = -10 + 10

Combine like terms: -67 + 10 = -57
-57 + 8n + 2n2 = -10 + 10

Combine like terms: -10 + 10 = 0
-57 + 8n + 2n2 = 0

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

Divide each side by '2'.
-28.5 + 4n + n2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + 4n + 28.5 + n2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + 4n + n2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + 4n + n2 = 0 + 28.5
4n + n2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
4n + n2 = 28.5

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 = 28.5 + 4

Reorder the terms:
4 + 4n + n2 = 28.5 + 4

Combine like terms: 28.5 + 4 = 32.5
4 + 4n + n2 = 32.5

Factor a perfect square on the left side:
(n + 2)(n + 2) = 32.5

Calculate the square root of the right side: 5.700877125

Break this problem into two subproblems by setting 
(n + 2) equal to 5.700877125 and -5.700877125.

Subproblem 1

n + 2 = 5.700877125 Simplifying n + 2 = 5.700877125 Reorder the terms: 2 + n = 5.700877125 Solving 2 + n = 5.700877125 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 = 5.700877125 + -2 Combine like terms: 2 + -2 = 0 0 + n = 5.700877125 + -2 n = 5.700877125 + -2 Combine like terms: 5.700877125 + -2 = 3.700877125 n = 3.700877125 Simplifying n = 3.700877125

Subproblem 2

n + 2 = -5.700877125 Simplifying n + 2 = -5.700877125 Reorder the terms: 2 + n = -5.700877125 Solving 2 + n = -5.700877125 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 = -5.700877125 + -2 Combine like terms: 2 + -2 = 0 0 + n = -5.700877125 + -2 n = -5.700877125 + -2 Combine like terms: -5.700877125 + -2 = -7.700877125 n = -7.700877125 Simplifying n = -7.700877125

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.700877125, -7.700877125}

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