0=3x^2-10x-349

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Solution for 0=3x^2-10x-349 equation:


Simplifying
0 = 3x2 + -10x + -349

Reorder the terms:
0 = -349 + -10x + 3x2

Solving
0 = -349 + -10x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 349 = 349
349 + 10x + -3x2 = -349 + -10x + 3x2 + 349 + 10x + -3x2

Reorder the terms:
349 + 10x + -3x2 = -349 + 349 + -10x + 10x + 3x2 + -3x2

Combine like terms: -349 + 349 = 0
349 + 10x + -3x2 = 0 + -10x + 10x + 3x2 + -3x2
349 + 10x + -3x2 = -10x + 10x + 3x2 + -3x2

Combine like terms: -10x + 10x = 0
349 + 10x + -3x2 = 0 + 3x2 + -3x2
349 + 10x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
349 + 10x + -3x2 = 0

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

Divide each side by '-3'.
-116.3333333 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '116.3333333' to each side of the equation.
-116.3333333 + -3.333333333x + 116.3333333 + x2 = 0 + 116.3333333

Reorder the terms:
-116.3333333 + 116.3333333 + -3.333333333x + x2 = 0 + 116.3333333

Combine like terms: -116.3333333 + 116.3333333 = 0.0000000
0.0000000 + -3.333333333x + x2 = 0 + 116.3333333
-3.333333333x + x2 = 0 + 116.3333333

Combine like terms: 0 + 116.3333333 = 116.3333333
-3.333333333x + x2 = 116.3333333

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 116.3333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 116.3333333 + 2.777777779

Combine like terms: 116.3333333 + 2.777777779 = 119.111111079
2.777777779 + -3.333333333x + x2 = 119.111111079

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 119.111111079

Calculate the square root of the right side: 10.913803694

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 10.913803694 and -10.913803694.

Subproblem 1

x + -1.666666667 = 10.913803694 Simplifying x + -1.666666667 = 10.913803694 Reorder the terms: -1.666666667 + x = 10.913803694 Solving -1.666666667 + x = 10.913803694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 10.913803694 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 10.913803694 + 1.666666667 x = 10.913803694 + 1.666666667 Combine like terms: 10.913803694 + 1.666666667 = 12.580470361 x = 12.580470361 Simplifying x = 12.580470361

Subproblem 2

x + -1.666666667 = -10.913803694 Simplifying x + -1.666666667 = -10.913803694 Reorder the terms: -1.666666667 + x = -10.913803694 Solving -1.666666667 + x = -10.913803694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -10.913803694 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -10.913803694 + 1.666666667 x = -10.913803694 + 1.666666667 Combine like terms: -10.913803694 + 1.666666667 = -9.247137027 x = -9.247137027 Simplifying x = -9.247137027

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.580470361, -9.247137027}

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