-8(2+7x)-x(-8+x)=

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Solution for -8(2+7x)-x(-8+x)= equation: 


Simplifying
-8(2 + 7x) + -1x(-8 + x) = 0
(2 * -8 + 7x * -8) + -1x(-8 + x) = 0
(-16 + -56x) + -1x(-8 + x) = 0
-16 + -56x + (-8 * -1x + x * -1x) = 0
-16 + -56x + (8x + -1x2) = 0

Combine like terms: -56x + 8x = -48x
-16 + -48x + -1x2 = 0

Solving
-16 + -48x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 48x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(16 + 48x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 48x + x2 = 0

Solving
16 + 48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 48x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 48x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 48x + x2 = 0 + -16
48x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
48x + x2 = -16

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = -16 + 576

Reorder the terms:
576 + 48x + x2 = -16 + 576

Combine like terms: -16 + 576 = 560
576 + 48x + x2 = 560

Factor a perfect square on the left side:
(x + 24)(x + 24) = 560

Calculate the square root of the right side: 23.664319132

Break this problem into two subproblems by setting 
(x + 24) equal to 23.664319132 and -23.664319132.


Subproblem 1
x + 24 = 23.664319132

Simplifying
x + 24 = 23.664319132

Reorder the terms:
24 + x = 23.664319132

Solving
24 + x = 23.664319132

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 23.664319132 + -24

Combine like terms: 24 + -24 = 0
0 + x = 23.664319132 + -24
x = 23.664319132 + -24

Combine like terms: 23.664319132 + -24 = -0.335680868
x = -0.335680868

Simplifying
x = -0.335680868


Subproblem 2
x + 24 = -23.664319132

Simplifying
x + 24 = -23.664319132

Reorder the terms:
24 + x = -23.664319132

Solving
24 + x = -23.664319132

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -23.664319132 + -24

Combine like terms: 24 + -24 = 0
0 + x = -23.664319132 + -24
x = -23.664319132 + -24

Combine like terms: -23.664319132 + -24 = -47.664319132
x = -47.664319132

Simplifying
x = -47.664319132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.335680868, -47.664319132}
Solution
x = {-0.335680868, -47.664319132}

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