6x^2-24x+4=200

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Solution for 6x^2-24x+4=200 equation: 


Simplifying
6x2 + -24x + 4 = 200

Reorder the terms:
4 + -24x + 6x2 = 200

Solving
4 + -24x + 6x2 = 200

Solving for variable 'x'.

Reorder the terms:
4 + -200 + -24x + 6x2 = 200 + -200

Combine like terms: 4 + -200 = -196
-196 + -24x + 6x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-196 + -24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-98 + -12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-98 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-98 + -12x + 3x2 = 0

Solving
-98 + -12x + 3x2 = 0

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

Divide each side by '3'.
-32.66666667 + -4x + x2 = 0

Move the constant term to the right:

Add '32.66666667' to each side of the equation.
-32.66666667 + -4x + 32.66666667 + x2 = 0 + 32.66666667

Reorder the terms:
-32.66666667 + 32.66666667 + -4x + x2 = 0 + 32.66666667

Combine like terms: -32.66666667 + 32.66666667 = 0.00000000
0.00000000 + -4x + x2 = 0 + 32.66666667
-4x + x2 = 0 + 32.66666667

Combine like terms: 0 + 32.66666667 = 32.66666667
-4x + x2 = 32.66666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 32.66666667 + 4

Reorder the terms:
4 + -4x + x2 = 32.66666667 + 4

Combine like terms: 32.66666667 + 4 = 36.66666667
4 + -4x + x2 = 36.66666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 36.66666667

Calculate the square root of the right side: 6.055300708

Break this problem into two subproblems by setting 
(x + -2) equal to 6.055300708 and -6.055300708.


Subproblem 1
x + -2 = 6.055300708

Simplifying
x + -2 = 6.055300708

Reorder the terms:
-2 + x = 6.055300708

Solving
-2 + x = 6.055300708

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.055300708 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.055300708 + 2
x = 6.055300708 + 2

Combine like terms: 6.055300708 + 2 = 8.055300708
x = 8.055300708

Simplifying
x = 8.055300708


Subproblem 2
x + -2 = -6.055300708

Simplifying
x + -2 = -6.055300708

Reorder the terms:
-2 + x = -6.055300708

Solving
-2 + x = -6.055300708

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.055300708 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.055300708 + 2
x = -6.055300708 + 2

Combine like terms: -6.055300708 + 2 = -4.055300708
x = -4.055300708

Simplifying
x = -4.055300708


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.055300708, -4.055300708}
Solution
x = {8.055300708, -4.055300708}

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