2x(x+5)=870

Solution for 2x(x+5)=870 equation:

Simplifying
2x(x + 5) = 870

Reorder the terms:
2x(5 + x) = 870
(5 * 2x + x * 2x) = 870
(10x + 2x2) = 870

Solving
10x + 2x2 = 870

Solving for variable 'x'.

Reorder the terms:
-870 + 10x + 2x2 = 870 + -870

Combine like terms: 870 + -870 = 0
-870 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-435 + 5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-435 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-435 + 5x + x2 = 0

Solving
-435 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '435' to each side of the equation.
-435 + 5x + 435 + x2 = 0 + 435

Reorder the terms:
-435 + 435 + 5x + x2 = 0 + 435

Combine like terms: -435 + 435 = 0
0 + 5x + x2 = 0 + 435
5x + x2 = 0 + 435

Combine like terms: 0 + 435 = 435
5x + x2 = 435

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 = 435 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 435 + 6.25

Combine like terms: 435 + 6.25 = 441.25
6.25 + 5x + x2 = 441.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 441.25

Calculate the square root of the right side: 21.005951538

Break this problem into two subproblems by setting 
(x + 2.5) equal to 21.005951538 and -21.005951538.

Subproblem 1
x + 2.5 = 21.005951538

Simplifying
x + 2.5 = 21.005951538

Reorder the terms:
2.5 + x = 21.005951538

Solving
2.5 + x = 21.005951538

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 = 21.005951538 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 21.005951538 + -2.5
x = 21.005951538 + -2.5

Combine like terms: 21.005951538 + -2.5 = 18.505951538
x = 18.505951538

Simplifying
x = 18.505951538

Subproblem 2
x + 2.5 = -21.005951538

Simplifying
x + 2.5 = -21.005951538

Reorder the terms:
2.5 + x = -21.005951538

Solving
2.5 + x = -21.005951538

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 = -21.005951538 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -21.005951538 + -2.5
x = -21.005951538 + -2.5

Combine like terms: -21.005951538 + -2.5 = -23.505951538
x = -23.505951538

Simplifying
x = -23.505951538

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.505951538, -23.505951538}
Solution
x = {18.505951538, -23.505951538}