3x^2-8x=200

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Solution for 3x^2-8x=200 equation: 


Simplifying
3x2 + -8x = 200

Reorder the terms:
-8x + 3x2 = 200

Solving
-8x + 3x2 = 200

Solving for variable 'x'.

Reorder the terms:
-200 + -8x + 3x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + -8x + 3x2 = 0

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

Divide each side by '3'.
-66.66666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '66.66666667' to each side of the equation.
-66.66666667 + -2.666666667x + 66.66666667 + x2 = 0 + 66.66666667

Reorder the terms:
-66.66666667 + 66.66666667 + -2.666666667x + x2 = 0 + 66.66666667

Combine like terms: -66.66666667 + 66.66666667 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 66.66666667
-2.666666667x + x2 = 0 + 66.66666667

Combine like terms: 0 + 66.66666667 = 66.66666667
-2.666666667x + x2 = 66.66666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 66.66666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 66.66666667 + 1.777777780

Combine like terms: 66.66666667 + 1.777777780 = 68.44444445
1.777777780 + -2.666666667x + x2 = 68.44444445

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 68.44444445

Calculate the square root of the right side: 8.273115764

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 8.273115764 and -8.273115764.


Subproblem 1
x + -1.333333334 = 8.273115764

Simplifying
x + -1.333333334 = 8.273115764

Reorder the terms:
-1.333333334 + x = 8.273115764

Solving
-1.333333334 + x = 8.273115764

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 8.273115764 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 8.273115764 + 1.333333334
x = 8.273115764 + 1.333333334

Combine like terms: 8.273115764 + 1.333333334 = 9.606449098
x = 9.606449098

Simplifying
x = 9.606449098


Subproblem 2
x + -1.333333334 = -8.273115764

Simplifying
x + -1.333333334 = -8.273115764

Reorder the terms:
-1.333333334 + x = -8.273115764

Solving
-1.333333334 + x = -8.273115764

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -8.273115764 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -8.273115764 + 1.333333334
x = -8.273115764 + 1.333333334

Combine like terms: -8.273115764 + 1.333333334 = -6.93978243
x = -6.93978243

Simplifying
x = -6.93978243


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.606449098, -6.93978243}

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