2x(5x+2)=10

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Solution for 2x(5x+2)=10 equation: 


Simplifying
2x(5x + 2) = 10

Reorder the terms:
2x(2 + 5x) = 10
(2 * 2x + 5x * 2x) = 10
(4x + 10x2) = 10

Solving
4x + 10x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 4x + 10x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 4x + 10x2 = 0

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

Ignore the factor 2.

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

Simplifying
-5 + 2x + 5x2 = 0

Solving
-5 + 2x + 5x2 = 0

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

Divide each side by '5'.
-1 + 0.4x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.4x + x2 = 0 + 1
0.4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.4x + x2 = 1

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 1 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 1 + 0.04

Combine like terms: 1 + 0.04 = 1.04
0.04 + 0.4x + x2 = 1.04

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 1.04

Calculate the square root of the right side: 1.019803903

Break this problem into two subproblems by setting 
(x + 0.2) equal to 1.019803903 and -1.019803903.


Subproblem 1
x + 0.2 = 1.019803903

Simplifying
x + 0.2 = 1.019803903

Reorder the terms:
0.2 + x = 1.019803903

Solving
0.2 + x = 1.019803903

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 1.019803903 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 1.019803903 + -0.2
x = 1.019803903 + -0.2

Combine like terms: 1.019803903 + -0.2 = 0.819803903
x = 0.819803903

Simplifying
x = 0.819803903


Subproblem 2
x + 0.2 = -1.019803903

Simplifying
x + 0.2 = -1.019803903

Reorder the terms:
0.2 + x = -1.019803903

Solving
0.2 + x = -1.019803903

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -1.019803903 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -1.019803903 + -0.2
x = -1.019803903 + -0.2

Combine like terms: -1.019803903 + -0.2 = -1.219803903
x = -1.219803903

Simplifying
x = -1.219803903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.819803903, -1.219803903}
Solution
x = {0.819803903, -1.219803903}

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