3x^2-3x=209

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Solution for 3x^2-3x=209 equation:


Simplifying
3x2 + -3x = 209

Reorder the terms:
-3x + 3x2 = 209

Solving
-3x + 3x2 = 209

Solving for variable 'x'.

Reorder the terms:
-209 + -3x + 3x2 = 209 + -209

Combine like terms: 209 + -209 = 0
-209 + -3x + 3x2 = 0

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

Divide each side by '3'.
-69.66666667 + -1x + x2 = 0

Move the constant term to the right:

Add '69.66666667' to each side of the equation.
-69.66666667 + -1x + 69.66666667 + x2 = 0 + 69.66666667

Reorder the terms:
-69.66666667 + 69.66666667 + -1x + x2 = 0 + 69.66666667

Combine like terms: -69.66666667 + 69.66666667 = 0.00000000
0.00000000 + -1x + x2 = 0 + 69.66666667
-1x + x2 = 0 + 69.66666667

Combine like terms: 0 + 69.66666667 = 69.66666667
-1x + x2 = 69.66666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 69.66666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 69.66666667 + 0.25

Combine like terms: 69.66666667 + 0.25 = 69.91666667
0.25 + -1x + x2 = 69.91666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 69.91666667

Calculate the square root of the right side: 8.361618663

Break this problem into two subproblems by setting 
(x + -0.5) equal to 8.361618663 and -8.361618663.

Subproblem 1

x + -0.5 = 8.361618663 Simplifying x + -0.5 = 8.361618663 Reorder the terms: -0.5 + x = 8.361618663 Solving -0.5 + x = 8.361618663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 8.361618663 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.361618663 + 0.5 x = 8.361618663 + 0.5 Combine like terms: 8.361618663 + 0.5 = 8.861618663 x = 8.861618663 Simplifying x = 8.861618663

Subproblem 2

x + -0.5 = -8.361618663 Simplifying x + -0.5 = -8.361618663 Reorder the terms: -0.5 + x = -8.361618663 Solving -0.5 + x = -8.361618663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -8.361618663 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.361618663 + 0.5 x = -8.361618663 + 0.5 Combine like terms: -8.361618663 + 0.5 = -7.861618663 x = -7.861618663 Simplifying x = -7.861618663

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.861618663, -7.861618663}

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