4x(4x+5)=580

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Solution for 4x(4x+5)=580 equation: 


Simplifying
4x(4x + 5) = 580

Reorder the terms:
4x(5 + 4x) = 580
(5 * 4x + 4x * 4x) = 580
(20x + 16x2) = 580

Solving
20x + 16x2 = 580

Solving for variable 'x'.

Reorder the terms:
-580 + 20x + 16x2 = 580 + -580

Combine like terms: 580 + -580 = 0
-580 + 20x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-145 + 5x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-145 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-145 + 5x + 4x2 = 0

Solving
-145 + 5x + 4x2 = 0

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

Divide each side by '4'.
-36.25 + 1.25x + x2 = 0

Move the constant term to the right:

Add '36.25' to each side of the equation.
-36.25 + 1.25x + 36.25 + x2 = 0 + 36.25

Reorder the terms:
-36.25 + 36.25 + 1.25x + x2 = 0 + 36.25

Combine like terms: -36.25 + 36.25 = 0.00
0.00 + 1.25x + x2 = 0 + 36.25
1.25x + x2 = 0 + 36.25

Combine like terms: 0 + 36.25 = 36.25
1.25x + x2 = 36.25

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 = 36.25 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 36.25 + 0.390625

Combine like terms: 36.25 + 0.390625 = 36.640625
0.390625 + 1.25x + x2 = 36.640625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 36.640625

Calculate the square root of the right side: 6.053150006

Break this problem into two subproblems by setting 
(x + 0.625) equal to 6.053150006 and -6.053150006.


Subproblem 1
x + 0.625 = 6.053150006

Simplifying
x + 0.625 = 6.053150006

Reorder the terms:
0.625 + x = 6.053150006

Solving
0.625 + x = 6.053150006

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 = 6.053150006 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 6.053150006 + -0.625
x = 6.053150006 + -0.625

Combine like terms: 6.053150006 + -0.625 = 5.428150006
x = 5.428150006

Simplifying
x = 5.428150006


Subproblem 2
x + 0.625 = -6.053150006

Simplifying
x + 0.625 = -6.053150006

Reorder the terms:
0.625 + x = -6.053150006

Solving
0.625 + x = -6.053150006

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 = -6.053150006 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -6.053150006 + -0.625
x = -6.053150006 + -0.625

Combine like terms: -6.053150006 + -0.625 = -6.678150006
x = -6.678150006

Simplifying
x = -6.678150006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.428150006, -6.678150006}
Solution
x = {5.428150006, -6.678150006}

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