x^2+8x-270=0

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Solution for x^2+8x-270=0 equation: 


Simplifying
x2 + 8x + -270 = 0

Reorder the terms:
-270 + 8x + x2 = 0

Solving
-270 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '270' to each side of the equation.
-270 + 8x + 270 + x2 = 0 + 270

Reorder the terms:
-270 + 270 + 8x + x2 = 0 + 270

Combine like terms: -270 + 270 = 0
0 + 8x + x2 = 0 + 270
8x + x2 = 0 + 270

Combine like terms: 0 + 270 = 270
8x + x2 = 270

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 = 270 + 16

Reorder the terms:
16 + 8x + x2 = 270 + 16

Combine like terms: 270 + 16 = 286
16 + 8x + x2 = 286

Factor a perfect square on the left side:
(x + 4)(x + 4) = 286

Calculate the square root of the right side: 16.911534525

Break this problem into two subproblems by setting 
(x + 4) equal to 16.911534525 and -16.911534525.


Subproblem 1
x + 4 = 16.911534525

Simplifying
x + 4 = 16.911534525

Reorder the terms:
4 + x = 16.911534525

Solving
4 + x = 16.911534525

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 = 16.911534525 + -4

Combine like terms: 4 + -4 = 0
0 + x = 16.911534525 + -4
x = 16.911534525 + -4

Combine like terms: 16.911534525 + -4 = 12.911534525
x = 12.911534525

Simplifying
x = 12.911534525


Subproblem 2
x + 4 = -16.911534525

Simplifying
x + 4 = -16.911534525

Reorder the terms:
4 + x = -16.911534525

Solving
4 + x = -16.911534525

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 = -16.911534525 + -4

Combine like terms: 4 + -4 = 0
0 + x = -16.911534525 + -4
x = -16.911534525 + -4

Combine like terms: -16.911534525 + -4 = -20.911534525
x = -20.911534525

Simplifying
x = -20.911534525


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.911534525, -20.911534525}

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