3x^2-311-4x=0

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Solution for 3x^2-311-4x=0 equation:


Simplifying
3x2 + -311 + -4x = 0

Reorder the terms:
-311 + -4x + 3x2 = 0

Solving
-311 + -4x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-103.6666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '103.6666667' to each side of the equation.
-103.6666667 + -1.333333333x + 103.6666667 + x2 = 0 + 103.6666667

Reorder the terms:
-103.6666667 + 103.6666667 + -1.333333333x + x2 = 0 + 103.6666667

Combine like terms: -103.6666667 + 103.6666667 = 0.0000000
0.0000000 + -1.333333333x + x2 = 0 + 103.6666667
-1.333333333x + x2 = 0 + 103.6666667

Combine like terms: 0 + 103.6666667 = 103.6666667
-1.333333333x + x2 = 103.6666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 103.6666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 103.6666667 + 0.4444444442

Combine like terms: 103.6666667 + 0.4444444442 = 104.1111111442
0.4444444442 + -1.333333333x + x2 = 104.1111111442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 104.1111111442

Calculate the square root of the right side: 10.203485245

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 10.203485245 and -10.203485245.

Subproblem 1

x + -0.6666666665 = 10.203485245 Simplifying x + -0.6666666665 = 10.203485245 Reorder the terms: -0.6666666665 + x = 10.203485245 Solving -0.6666666665 + x = 10.203485245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 10.203485245 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 10.203485245 + 0.6666666665 x = 10.203485245 + 0.6666666665 Combine like terms: 10.203485245 + 0.6666666665 = 10.8701519115 x = 10.8701519115 Simplifying x = 10.8701519115

Subproblem 2

x + -0.6666666665 = -10.203485245 Simplifying x + -0.6666666665 = -10.203485245 Reorder the terms: -0.6666666665 + x = -10.203485245 Solving -0.6666666665 + x = -10.203485245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -10.203485245 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -10.203485245 + 0.6666666665 x = -10.203485245 + 0.6666666665 Combine like terms: -10.203485245 + 0.6666666665 = -9.5368185785 x = -9.5368185785 Simplifying x = -9.5368185785

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.8701519115, -9.5368185785}

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