4x(x-5)=46

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Solution for 4x(x-5)=46 equation: 


Simplifying
4x(x + -5) = 46

Reorder the terms:
4x(-5 + x) = 46
(-5 * 4x + x * 4x) = 46
(-20x + 4x2) = 46

Solving
-20x + 4x2 = 46

Solving for variable 'x'.

Reorder the terms:
-46 + -20x + 4x2 = 46 + -46

Combine like terms: 46 + -46 = 0
-46 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + -10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-23 + -10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-23 + -10x + 2x2 = 0

Solving
-23 + -10x + 2x2 = 0

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

Divide each side by '2'.
-11.5 + -5x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -5x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -5x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -5x + x2 = 0 + 11.5
-5x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
-5x + x2 = 11.5

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 = 11.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 11.5 + 6.25

Combine like terms: 11.5 + 6.25 = 17.75
6.25 + -5x + x2 = 17.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 17.75

Calculate the square root of the right side: 4.213074887

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.213074887 and -4.213074887.


Subproblem 1
x + -2.5 = 4.213074887

Simplifying
x + -2.5 = 4.213074887

Reorder the terms:
-2.5 + x = 4.213074887

Solving
-2.5 + x = 4.213074887

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 = 4.213074887 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.213074887 + 2.5
x = 4.213074887 + 2.5

Combine like terms: 4.213074887 + 2.5 = 6.713074887
x = 6.713074887

Simplifying
x = 6.713074887


Subproblem 2
x + -2.5 = -4.213074887

Simplifying
x + -2.5 = -4.213074887

Reorder the terms:
-2.5 + x = -4.213074887

Solving
-2.5 + x = -4.213074887

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 = -4.213074887 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.213074887 + 2.5
x = -4.213074887 + 2.5

Combine like terms: -4.213074887 + 2.5 = -1.713074887
x = -1.713074887

Simplifying
x = -1.713074887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.713074887, -1.713074887}
Solution
x = {6.713074887, -1.713074887}

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