5x(10x-5)=90

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Solution for 5x(10x-5)=90 equation: 


Simplifying
5x(10x + -5) = 90

Reorder the terms:
5x(-5 + 10x) = 90
(-5 * 5x + 10x * 5x) = 90
(-25x + 50x2) = 90

Solving
-25x + 50x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -25x + 50x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -25x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -5x + 10x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-18 + -5x + 10x2)' equal to zero and attempt to solve:

Simplifying
-18 + -5x + 10x2 = 0

Solving
-18 + -5x + 10x2 = 0

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

Divide each side by '10'.
-1.8 + -0.5x + x2 = 0.0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -0.5x + 1.8 + x2 = 0.0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -0.5x + x2 = 0.0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -0.5x + x2 = 0.0 + 1.8
-0.5x + x2 = 0.0 + 1.8

Combine like terms: 0.0 + 1.8 = 1.8
-0.5x + x2 = 1.8

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 1.8 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 1.8 + 0.0625

Combine like terms: 1.8 + 0.0625 = 1.8625
0.0625 + -0.5x + x2 = 1.8625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 1.8625

Calculate the square root of the right side: 1.364734406

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.364734406 and -1.364734406.


Subproblem 1
x + -0.25 = 1.364734406

Simplifying
x + -0.25 = 1.364734406

Reorder the terms:
-0.25 + x = 1.364734406

Solving
-0.25 + x = 1.364734406

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.364734406 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.364734406 + 0.25
x = 1.364734406 + 0.25

Combine like terms: 1.364734406 + 0.25 = 1.614734406
x = 1.614734406

Simplifying
x = 1.614734406


Subproblem 2
x + -0.25 = -1.364734406

Simplifying
x + -0.25 = -1.364734406

Reorder the terms:
-0.25 + x = -1.364734406

Solving
-0.25 + x = -1.364734406

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.364734406 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.364734406 + 0.25
x = -1.364734406 + 0.25

Combine like terms: -1.364734406 + 0.25 = -1.114734406
x = -1.114734406

Simplifying
x = -1.114734406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.614734406, -1.114734406}
Solution
x = {1.614734406, -1.114734406}

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