2x(4x+5)=4

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Solution for 2x(4x+5)=4 equation: 


Simplifying
2x(4x + 5) = 4

Reorder the terms:
2x(5 + 4x) = 4
(5 * 2x + 4x * 2x) = 4
(10x + 8x2) = 4

Solving
10x + 8x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 10x + 8x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 10x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-2 + 5x + 4x2 = 0

Solving
-2 + 5x + 4x2 = 0

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

Divide each side by '4'.
-0.5 + 1.25x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.25x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.25x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.25x + x2 = 0 + 0.5
1.25x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.25x + x2 = 0.5

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 0.5 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 0.5 + 0.390625

Combine like terms: 0.5 + 0.390625 = 0.890625
0.390625 + 1.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + 0.625) equal to 0.943729304 and -0.943729304.


Subproblem 1
x + 0.625 = 0.943729304

Simplifying
x + 0.625 = 0.943729304

Reorder the terms:
0.625 + x = 0.943729304

Solving
0.625 + x = 0.943729304

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 0.943729304 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 0.943729304 + -0.625
x = 0.943729304 + -0.625

Combine like terms: 0.943729304 + -0.625 = 0.318729304
x = 0.318729304

Simplifying
x = 0.318729304


Subproblem 2
x + 0.625 = -0.943729304

Simplifying
x + 0.625 = -0.943729304

Reorder the terms:
0.625 + x = -0.943729304

Solving
0.625 + x = -0.943729304

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -0.943729304 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -0.943729304 + -0.625
x = -0.943729304 + -0.625

Combine like terms: -0.943729304 + -0.625 = -1.568729304
x = -1.568729304

Simplifying
x = -1.568729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.318729304, -1.568729304}
Solution
x = {0.318729304, -1.568729304}

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