200x^2-12x-12=0

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Solution for 200x^2-12x-12=0 equation: 


Simplifying
200x2 + -12x + -12 = 0

Reorder the terms:
-12 + -12x + 200x2 = 0

Solving
-12 + -12x + 200x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -3x + 50x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -3x + 50x2)' equal to zero and attempt to solve:

Simplifying
-3 + -3x + 50x2 = 0

Solving
-3 + -3x + 50x2 = 0

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

Divide each side by '50'.
-0.06 + -0.06x + x2 = 0.0

Move the constant term to the right:

Add '0.06' to each side of the equation.
-0.06 + -0.06x + 0.06 + x2 = 0.0 + 0.06

Reorder the terms:
-0.06 + 0.06 + -0.06x + x2 = 0.0 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.00 + -0.06x + x2 = 0.0 + 0.06
-0.06x + x2 = 0.0 + 0.06

Combine like terms: 0.0 + 0.06 = 0.06
-0.06x + x2 = 0.06

The x term is -0.06x.  Take half its coefficient (-0.03).
Square it (0.0009) and add it to both sides.

Add '0.0009' to each side of the equation.
-0.06x + 0.0009 + x2 = 0.06 + 0.0009

Reorder the terms:
0.0009 + -0.06x + x2 = 0.06 + 0.0009

Combine like terms: 0.06 + 0.0009 = 0.0609
0.0009 + -0.06x + x2 = 0.0609

Factor a perfect square on the left side:
(x + -0.03)(x + -0.03) = 0.0609

Calculate the square root of the right side: 0.246779254

Break this problem into two subproblems by setting 
(x + -0.03) equal to 0.246779254 and -0.246779254.


Subproblem 1
x + -0.03 = 0.246779254

Simplifying
x + -0.03 = 0.246779254

Reorder the terms:
-0.03 + x = 0.246779254

Solving
-0.03 + x = 0.246779254

Solving for variable 'x'.

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

Add '0.03' to each side of the equation.
-0.03 + 0.03 + x = 0.246779254 + 0.03

Combine like terms: -0.03 + 0.03 = 0.00
0.00 + x = 0.246779254 + 0.03
x = 0.246779254 + 0.03

Combine like terms: 0.246779254 + 0.03 = 0.276779254
x = 0.276779254

Simplifying
x = 0.276779254


Subproblem 2
x + -0.03 = -0.246779254

Simplifying
x + -0.03 = -0.246779254

Reorder the terms:
-0.03 + x = -0.246779254

Solving
-0.03 + x = -0.246779254

Solving for variable 'x'.

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

Add '0.03' to each side of the equation.
-0.03 + 0.03 + x = -0.246779254 + 0.03

Combine like terms: -0.03 + 0.03 = 0.00
0.00 + x = -0.246779254 + 0.03
x = -0.246779254 + 0.03

Combine like terms: -0.246779254 + 0.03 = -0.216779254
x = -0.216779254

Simplifying
x = -0.216779254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.276779254, -0.216779254}
Solution
x = {0.276779254, -0.216779254}

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