X^2+8X-280=0

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Solution for X^2+8X-280=0 equation: 


Simplifying
X2 + 8X + -280 = 0

Reorder the terms:
-280 + 8X + X2 = 0

Solving
-280 + 8X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 8X + 280 + X2 = 0 + 280

Reorder the terms:
-280 + 280 + 8X + X2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 8X + X2 = 0 + 280
8X + X2 = 0 + 280

Combine like terms: 0 + 280 = 280
8X + X2 = 280

The X term is 8X.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8X + 16 + X2 = 280 + 16

Reorder the terms:
16 + 8X + X2 = 280 + 16

Combine like terms: 280 + 16 = 296
16 + 8X + X2 = 296

Factor a perfect square on the left side:
(X + 4)(X + 4) = 296

Calculate the square root of the right side: 17.204650534

Break this problem into two subproblems by setting 
(X + 4) equal to 17.204650534 and -17.204650534.


Subproblem 1
X + 4 = 17.204650534

Simplifying
X + 4 = 17.204650534

Reorder the terms:
4 + X = 17.204650534

Solving
4 + X = 17.204650534

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + X = 17.204650534 + -4

Combine like terms: 4 + -4 = 0
0 + X = 17.204650534 + -4
X = 17.204650534 + -4

Combine like terms: 17.204650534 + -4 = 13.204650534
X = 13.204650534

Simplifying
X = 13.204650534


Subproblem 2
X + 4 = -17.204650534

Simplifying
X + 4 = -17.204650534

Reorder the terms:
4 + X = -17.204650534

Solving
4 + X = -17.204650534

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + X = -17.204650534 + -4

Combine like terms: 4 + -4 = 0
0 + X = -17.204650534 + -4
X = -17.204650534 + -4

Combine like terms: -17.204650534 + -4 = -21.204650534
X = -21.204650534

Simplifying
X = -21.204650534


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {13.204650534, -21.204650534}

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