2x(30x-2)=2

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Solution for 2x(30x-2)=2 equation: 


Simplifying
2x(30x + -2) = 2

Reorder the terms:
2x(-2 + 30x) = 2
(-2 * 2x + 30x * 2x) = 2
(-4x + 60x2) = 2

Solving
-4x + 60x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -4x + 60x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -4x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2x + 30x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2x + 30x2)' equal to zero and attempt to solve:

Simplifying
-1 + -2x + 30x2 = 0

Solving
-1 + -2x + 30x2 = 0

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

Divide each side by '30'.
-0.03333333333 + -0.06666666667x + x2 = 0.0

Move the constant term to the right:

Add '0.03333333333' to each side of the equation.
-0.03333333333 + -0.06666666667x + 0.03333333333 + x2 = 0.0 + 0.03333333333

Reorder the terms:
-0.03333333333 + 0.03333333333 + -0.06666666667x + x2 = 0.0 + 0.03333333333

Combine like terms: -0.03333333333 + 0.03333333333 = 0.00000000000
0.00000000000 + -0.06666666667x + x2 = 0.0 + 0.03333333333
-0.06666666667x + x2 = 0.0 + 0.03333333333

Combine like terms: 0.0 + 0.03333333333 = 0.03333333333
-0.06666666667x + x2 = 0.03333333333

The x term is -0.06666666667x.  Take half its coefficient (-0.03333333334).
Square it (0.001111111112) and add it to both sides.

Add '0.001111111112' to each side of the equation.
-0.06666666667x + 0.001111111112 + x2 = 0.03333333333 + 0.001111111112

Reorder the terms:
0.001111111112 + -0.06666666667x + x2 = 0.03333333333 + 0.001111111112

Combine like terms: 0.03333333333 + 0.001111111112 = 0.034444444442
0.001111111112 + -0.06666666667x + x2 = 0.034444444442

Factor a perfect square on the left side:
(x + -0.03333333334)(x + -0.03333333334) = 0.034444444442

Calculate the square root of the right side: 0.185592145

Break this problem into two subproblems by setting 
(x + -0.03333333334) equal to 0.185592145 and -0.185592145.


Subproblem 1
x + -0.03333333334 = 0.185592145

Simplifying
x + -0.03333333334 = 0.185592145

Reorder the terms:
-0.03333333334 + x = 0.185592145

Solving
-0.03333333334 + x = 0.185592145

Solving for variable 'x'.

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

Add '0.03333333334' to each side of the equation.
-0.03333333334 + 0.03333333334 + x = 0.185592145 + 0.03333333334

Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000
0.00000000000 + x = 0.185592145 + 0.03333333334
x = 0.185592145 + 0.03333333334

Combine like terms: 0.185592145 + 0.03333333334 = 0.21892547834
x = 0.21892547834

Simplifying
x = 0.21892547834


Subproblem 2
x + -0.03333333334 = -0.185592145

Simplifying
x + -0.03333333334 = -0.185592145

Reorder the terms:
-0.03333333334 + x = -0.185592145

Solving
-0.03333333334 + x = -0.185592145

Solving for variable 'x'.

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

Add '0.03333333334' to each side of the equation.
-0.03333333334 + 0.03333333334 + x = -0.185592145 + 0.03333333334

Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000
0.00000000000 + x = -0.185592145 + 0.03333333334
x = -0.185592145 + 0.03333333334

Combine like terms: -0.185592145 + 0.03333333334 = -0.15225881166
x = -0.15225881166

Simplifying
x = -0.15225881166


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.21892547834, -0.15225881166}
Solution
x = {0.21892547834, -0.15225881166}

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