n^2+17n-140=2n-4n

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Solution for n^2+17n-140=2n-4n equation:


Simplifying
n2 + 17n + -140 = 2n + -4n

Reorder the terms:
-140 + 17n + n2 = 2n + -4n

Combine like terms: 2n + -4n = -2n
-140 + 17n + n2 = -2n

Solving
-140 + 17n + n2 = -2n

Solving for variable 'n'.

Reorder the terms:
-140 + 17n + 2n + n2 = -2n + 2n

Combine like terms: 17n + 2n = 19n
-140 + 19n + n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-140 + 19n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 19n + 140 + n2 = 0 + 140

Reorder the terms:
-140 + 140 + 19n + n2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 19n + n2 = 0 + 140
19n + n2 = 0 + 140

Combine like terms: 0 + 140 = 140
19n + n2 = 140

The n term is 19n.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19n + 90.25 + n2 = 140 + 90.25

Reorder the terms:
90.25 + 19n + n2 = 140 + 90.25

Combine like terms: 140 + 90.25 = 230.25
90.25 + 19n + n2 = 230.25

Factor a perfect square on the left side:
(n + 9.5)(n + 9.5) = 230.25

Calculate the square root of the right side: 15.173990905

Break this problem into two subproblems by setting 
(n + 9.5) equal to 15.173990905 and -15.173990905.

Subproblem 1

n + 9.5 = 15.173990905 Simplifying n + 9.5 = 15.173990905 Reorder the terms: 9.5 + n = 15.173990905 Solving 9.5 + n = 15.173990905 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = 15.173990905 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = 15.173990905 + -9.5 n = 15.173990905 + -9.5 Combine like terms: 15.173990905 + -9.5 = 5.673990905 n = 5.673990905 Simplifying n = 5.673990905

Subproblem 2

n + 9.5 = -15.173990905 Simplifying n + 9.5 = -15.173990905 Reorder the terms: 9.5 + n = -15.173990905 Solving 9.5 + n = -15.173990905 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = -15.173990905 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = -15.173990905 + -9.5 n = -15.173990905 + -9.5 Combine like terms: -15.173990905 + -9.5 = -24.673990905 n = -24.673990905 Simplifying n = -24.673990905

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.673990905, -24.673990905}

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