2x(5x-1)=90

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Solution for 2x(5x-1)=90 equation: 


Simplifying
2x(5x + -1) = 90

Reorder the terms:
2x(-1 + 5x) = 90
(-1 * 2x + 5x * 2x) = 90
(-2x + 10x2) = 90

Solving
-2x + 10x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -2x + 10x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -2x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -1x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + -1x + 5x2)' equal to zero and attempt to solve:

Simplifying
-45 + -1x + 5x2 = 0

Solving
-45 + -1x + 5x2 = 0

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

Divide each side by '5'.
-9 + -0.2x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -0.2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -0.2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -0.2x + x2 = 0 + 9
-0.2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-0.2x + x2 = 9

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = 9 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 9 + 0.01

Combine like terms: 9 + 0.01 = 9.01
0.01 + -0.2x + x2 = 9.01

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 9.01

Calculate the square root of the right side: 3.001666204

Break this problem into two subproblems by setting 
(x + -0.1) equal to 3.001666204 and -3.001666204.


Subproblem 1
x + -0.1 = 3.001666204

Simplifying
x + -0.1 = 3.001666204

Reorder the terms:
-0.1 + x = 3.001666204

Solving
-0.1 + x = 3.001666204

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = 3.001666204 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = 3.001666204 + 0.1
x = 3.001666204 + 0.1

Combine like terms: 3.001666204 + 0.1 = 3.101666204
x = 3.101666204

Simplifying
x = 3.101666204


Subproblem 2
x + -0.1 = -3.001666204

Simplifying
x + -0.1 = -3.001666204

Reorder the terms:
-0.1 + x = -3.001666204

Solving
-0.1 + x = -3.001666204

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = -3.001666204 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = -3.001666204 + 0.1
x = -3.001666204 + 0.1

Combine like terms: -3.001666204 + 0.1 = -2.901666204
x = -2.901666204

Simplifying
x = -2.901666204


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.101666204, -2.901666204}
Solution
x = {3.101666204, -2.901666204}

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