2x(x+8)=110

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Solution for 2x(x+8)=110 equation: 


Simplifying
2x(x + 8) = 110

Reorder the terms:
2x(8 + x) = 110
(8 * 2x + x * 2x) = 110
(16x + 2x2) = 110

Solving
16x + 2x2 = 110

Solving for variable 'x'.

Reorder the terms:
-110 + 16x + 2x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-55 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-55 + 8x + x2 = 0

Solving
-55 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 8x + 55 + x2 = 0 + 55

Reorder the terms:
-55 + 55 + 8x + x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 8x + x2 = 0 + 55
8x + x2 = 0 + 55

Combine like terms: 0 + 55 = 55
8x + x2 = 55

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 = 55 + 16

Reorder the terms:
16 + 8x + x2 = 55 + 16

Combine like terms: 55 + 16 = 71
16 + 8x + x2 = 71

Factor a perfect square on the left side:
(x + 4)(x + 4) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 4) equal to 8.426149773 and -8.426149773.


Subproblem 1
x + 4 = 8.426149773

Simplifying
x + 4 = 8.426149773

Reorder the terms:
4 + x = 8.426149773

Solving
4 + x = 8.426149773

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 = 8.426149773 + -4

Combine like terms: 4 + -4 = 0
0 + x = 8.426149773 + -4
x = 8.426149773 + -4

Combine like terms: 8.426149773 + -4 = 4.426149773
x = 4.426149773

Simplifying
x = 4.426149773


Subproblem 2
x + 4 = -8.426149773

Simplifying
x + 4 = -8.426149773

Reorder the terms:
4 + x = -8.426149773

Solving
4 + x = -8.426149773

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 = -8.426149773 + -4

Combine like terms: 4 + -4 = 0
0 + x = -8.426149773 + -4
x = -8.426149773 + -4

Combine like terms: -8.426149773 + -4 = -12.426149773
x = -12.426149773

Simplifying
x = -12.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.426149773, -12.426149773}
Solution
x = {4.426149773, -12.426149773}

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