n^2+13n-30=-7

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Solution for n^2+13n-30=-7 equation:


Simplifying
n2 + 13n + -30 = -7

Reorder the terms:
-30 + 13n + n2 = -7

Solving
-30 + 13n + n2 = -7

Solving for variable 'n'.

Reorder the terms:
-30 + 7 + 13n + n2 = -7 + 7

Combine like terms: -30 + 7 = -23
-23 + 13n + n2 = -7 + 7

Combine like terms: -7 + 7 = 0
-23 + 13n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 13n + 23 + n2 = 0 + 23

Reorder the terms:
-23 + 23 + 13n + n2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 13n + n2 = 0 + 23
13n + n2 = 0 + 23

Combine like terms: 0 + 23 = 23
13n + n2 = 23

The n term is 13n.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13n + 42.25 + n2 = 23 + 42.25

Reorder the terms:
42.25 + 13n + n2 = 23 + 42.25

Combine like terms: 23 + 42.25 = 65.25
42.25 + 13n + n2 = 65.25

Factor a perfect square on the left side:
(n + 6.5)(n + 6.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(n + 6.5) equal to 8.077747211 and -8.077747211.

Subproblem 1

n + 6.5 = 8.077747211 Simplifying n + 6.5 = 8.077747211 Reorder the terms: 6.5 + n = 8.077747211 Solving 6.5 + n = 8.077747211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = 8.077747211 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = 8.077747211 + -6.5 n = 8.077747211 + -6.5 Combine like terms: 8.077747211 + -6.5 = 1.577747211 n = 1.577747211 Simplifying n = 1.577747211

Subproblem 2

n + 6.5 = -8.077747211 Simplifying n + 6.5 = -8.077747211 Reorder the terms: 6.5 + n = -8.077747211 Solving 6.5 + n = -8.077747211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = -8.077747211 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = -8.077747211 + -6.5 n = -8.077747211 + -6.5 Combine like terms: -8.077747211 + -6.5 = -14.577747211 n = -14.577747211 Simplifying n = -14.577747211

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.577747211, -14.577747211}

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