8x+10=2x(x+9)

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Solution for 8x+10=2x(x+9) equation: 


Simplifying
8x + 10 = 2x(x + 9)

Reorder the terms:
10 + 8x = 2x(x + 9)

Reorder the terms:
10 + 8x = 2x(9 + x)
10 + 8x = (9 * 2x + x * 2x)
10 + 8x = (18x + 2x2)

Solving
10 + 8x = 18x + 2x2

Solving for variable 'x'.

Combine like terms: 8x + -18x = -10x
10 + -10x + -2x2 = 18x + 2x2 + -18x + -2x2

Reorder the terms:
10 + -10x + -2x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
10 + -10x + -2x2 = 0 + 2x2 + -2x2
10 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -5x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -5x + -1x2 = 0

Solving
5 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 5x + x2 = 0 + 5
5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
5x + x2 = 5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5x + x2 = 11.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 2.5 = 3.354101966

Simplifying
x + 2.5 = 3.354101966

Reorder the terms:
2.5 + x = 3.354101966

Solving
2.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.354101966 + -2.5
x = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
x = 0.854101966

Simplifying
x = 0.854101966


Subproblem 2
x + 2.5 = -3.354101966

Simplifying
x + 2.5 = -3.354101966

Reorder the terms:
2.5 + x = -3.354101966

Solving
2.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.354101966 + -2.5
x = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
x = -5.854101966

Simplifying
x = -5.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.854101966, -5.854101966}
Solution
x = {0.854101966, -5.854101966}

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