2x*(x+10)=140

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Solution for 2x*(x+10)=140 equation: 


Simplifying
2x(x + 10) = 140

Reorder the terms:
2x(10 + x) = 140
(10 * 2x + x * 2x) = 140
(20x + 2x2) = 140

Solving
20x + 2x2 = 140

Solving for variable 'x'.

Reorder the terms:
-140 + 20x + 2x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-70 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-70 + 10x + x2 = 0

Solving
-70 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 10x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 10x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 10x + x2 = 0 + 70
10x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
10x + x2 = 70

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 70 + 25

Reorder the terms:
25 + 10x + x2 = 70 + 25

Combine like terms: 70 + 25 = 95
25 + 10x + x2 = 95

Factor a perfect square on the left side:
(x + 5)(x + 5) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(x + 5) equal to 9.746794345 and -9.746794345.


Subproblem 1
x + 5 = 9.746794345

Simplifying
x + 5 = 9.746794345

Reorder the terms:
5 + x = 9.746794345

Solving
5 + x = 9.746794345

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 9.746794345 + -5

Combine like terms: 5 + -5 = 0
0 + x = 9.746794345 + -5
x = 9.746794345 + -5

Combine like terms: 9.746794345 + -5 = 4.746794345
x = 4.746794345

Simplifying
x = 4.746794345


Subproblem 2
x + 5 = -9.746794345

Simplifying
x + 5 = -9.746794345

Reorder the terms:
5 + x = -9.746794345

Solving
5 + x = -9.746794345

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -9.746794345 + -5

Combine like terms: 5 + -5 = 0
0 + x = -9.746794345 + -5
x = -9.746794345 + -5

Combine like terms: -9.746794345 + -5 = -14.746794345
x = -14.746794345

Simplifying
x = -14.746794345


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.746794345, -14.746794345}
Solution
x = {4.746794345, -14.746794345}

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