x(10+2x)=40

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Solution for x(10+2x)=40 equation: 


Simplifying
x(10 + 2x) = 40
(10 * x + 2x * x) = 40
(10x + 2x2) = 40

Solving
10x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 10x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 5x + x2 = 0

Solving
-20 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 5x + x2 = 0 + 20
5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
5x + x2 = 20

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 = 20 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 20 + 6.25

Combine like terms: 20 + 6.25 = 26.25
6.25 + 5x + x2 = 26.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
x + 2.5 = 5.123475383

Simplifying
x + 2.5 = 5.123475383

Reorder the terms:
2.5 + x = 5.123475383

Solving
2.5 + x = 5.123475383

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 = 5.123475383 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.123475383 + -2.5
x = 5.123475383 + -2.5

Combine like terms: 5.123475383 + -2.5 = 2.623475383
x = 2.623475383

Simplifying
x = 2.623475383


Subproblem 2
x + 2.5 = -5.123475383

Simplifying
x + 2.5 = -5.123475383

Reorder the terms:
2.5 + x = -5.123475383

Solving
2.5 + x = -5.123475383

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 = -5.123475383 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.123475383 + -2.5
x = -5.123475383 + -2.5

Combine like terms: -5.123475383 + -2.5 = -7.623475383
x = -7.623475383

Simplifying
x = -7.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.623475383, -7.623475383}
Solution
x = {2.623475383, -7.623475383}

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