n^2+49n-498=0

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Solution for n^2+49n-498=0 equation:


Simplifying
n2 + 49n + -498 = 0

Reorder the terms:
-498 + 49n + n2 = 0

Solving
-498 + 49n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '498' to each side of the equation.
-498 + 49n + 498 + n2 = 0 + 498

Reorder the terms:
-498 + 498 + 49n + n2 = 0 + 498

Combine like terms: -498 + 498 = 0
0 + 49n + n2 = 0 + 498
49n + n2 = 0 + 498

Combine like terms: 0 + 498 = 498
49n + n2 = 498

The n term is 49n.  Take half its coefficient (24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
49n + 600.25 + n2 = 498 + 600.25

Reorder the terms:
600.25 + 49n + n2 = 498 + 600.25

Combine like terms: 498 + 600.25 = 1098.25
600.25 + 49n + n2 = 1098.25

Factor a perfect square on the left side:
(n + 24.5)(n + 24.5) = 1098.25

Calculate the square root of the right side: 33.13985516

Break this problem into two subproblems by setting 
(n + 24.5) equal to 33.13985516 and -33.13985516.

Subproblem 1

n + 24.5 = 33.13985516 Simplifying n + 24.5 = 33.13985516 Reorder the terms: 24.5 + n = 33.13985516 Solving 24.5 + n = 33.13985516 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + n = 33.13985516 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + n = 33.13985516 + -24.5 n = 33.13985516 + -24.5 Combine like terms: 33.13985516 + -24.5 = 8.63985516 n = 8.63985516 Simplifying n = 8.63985516

Subproblem 2

n + 24.5 = -33.13985516 Simplifying n + 24.5 = -33.13985516 Reorder the terms: 24.5 + n = -33.13985516 Solving 24.5 + n = -33.13985516 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + n = -33.13985516 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + n = -33.13985516 + -24.5 n = -33.13985516 + -24.5 Combine like terms: -33.13985516 + -24.5 = -57.63985516 n = -57.63985516 Simplifying n = -57.63985516

Solution

The solution to the problem is based on the solutions from the subproblems. n = {8.63985516, -57.63985516}

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