n^2+7n-270=0

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Solution for n^2+7n-270=0 equation:


Simplifying
n2 + 7n + -270 = 0

Reorder the terms:
-270 + 7n + n2 = 0

Solving
-270 + 7n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '270' to each side of the equation.
-270 + 7n + 270 + n2 = 0 + 270

Reorder the terms:
-270 + 270 + 7n + n2 = 0 + 270

Combine like terms: -270 + 270 = 0
0 + 7n + n2 = 0 + 270
7n + n2 = 0 + 270

Combine like terms: 0 + 270 = 270
7n + n2 = 270

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 270 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 270 + 12.25

Combine like terms: 270 + 12.25 = 282.25
12.25 + 7n + n2 = 282.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(n + 3.5) equal to 16.800297616 and -16.800297616.

Subproblem 1

n + 3.5 = 16.800297616 Simplifying n + 3.5 = 16.800297616 Reorder the terms: 3.5 + n = 16.800297616 Solving 3.5 + n = 16.800297616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 16.800297616 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 16.800297616 + -3.5 n = 16.800297616 + -3.5 Combine like terms: 16.800297616 + -3.5 = 13.300297616 n = 13.300297616 Simplifying n = 13.300297616

Subproblem 2

n + 3.5 = -16.800297616 Simplifying n + 3.5 = -16.800297616 Reorder the terms: 3.5 + n = -16.800297616 Solving 3.5 + n = -16.800297616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -16.800297616 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -16.800297616 + -3.5 n = -16.800297616 + -3.5 Combine like terms: -16.800297616 + -3.5 = -20.300297616 n = -20.300297616 Simplifying n = -20.300297616

Solution

The solution to the problem is based on the solutions from the subproblems. n = {13.300297616, -20.300297616}

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