2x(4x-5)=20

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Solution for 2x(4x-5)=20 equation: 


Simplifying
2x(4x + -5) = 20

Reorder the terms:
2x(-5 + 4x) = 20
(-5 * 2x + 4x * 2x) = 20
(-10x + 8x2) = 20

Solving
-10x + 8x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -10x + 8x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -10x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -5x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-10 + -5x + 4x2 = 0

Solving
-10 + -5x + 4x2 = 0

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

Divide each side by '4'.
-2.5 + -1.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1.25x + x2 = 0 + 2.5
-1.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1.25x + x2 = 2.5

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 = 2.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 2.5 + 0.390625

Combine like terms: 2.5 + 0.390625 = 2.890625
0.390625 + -1.25x + x2 = 2.890625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(x + -0.625) equal to 1.700183814 and -1.700183814.


Subproblem 1
x + -0.625 = 1.700183814

Simplifying
x + -0.625 = 1.700183814

Reorder the terms:
-0.625 + x = 1.700183814

Solving
-0.625 + x = 1.700183814

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 = 1.700183814 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 1.700183814 + 0.625
x = 1.700183814 + 0.625

Combine like terms: 1.700183814 + 0.625 = 2.325183814
x = 2.325183814

Simplifying
x = 2.325183814


Subproblem 2
x + -0.625 = -1.700183814

Simplifying
x + -0.625 = -1.700183814

Reorder the terms:
-0.625 + x = -1.700183814

Solving
-0.625 + x = -1.700183814

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 = -1.700183814 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -1.700183814 + 0.625
x = -1.700183814 + 0.625

Combine like terms: -1.700183814 + 0.625 = -1.075183814
x = -1.075183814

Simplifying
x = -1.075183814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.325183814, -1.075183814}
Solution
x = {2.325183814, -1.075183814}

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