3x^2-2x-190=0

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Solution for 3x^2-2x-190=0 equation:


Simplifying
3x2 + -2x + -190 = 0

Reorder the terms:
-190 + -2x + 3x2 = 0

Solving
-190 + -2x + 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'.
-63.33333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '63.33333333' to each side of the equation.
-63.33333333 + -0.6666666667x + 63.33333333 + x2 = 0 + 63.33333333

Reorder the terms:
-63.33333333 + 63.33333333 + -0.6666666667x + x2 = 0 + 63.33333333

Combine like terms: -63.33333333 + 63.33333333 = 0.00000000
0.00000000 + -0.6666666667x + x2 = 0 + 63.33333333
-0.6666666667x + x2 = 0 + 63.33333333

Combine like terms: 0 + 63.33333333 = 63.33333333
-0.6666666667x + x2 = 63.33333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 63.33333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 63.33333333 + 0.1111111112

Combine like terms: 63.33333333 + 0.1111111112 = 63.4444444412
0.1111111112 + -0.6666666667x + x2 = 63.4444444412

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 63.4444444412

Calculate the square root of the right side: 7.965202097

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 7.965202097 and -7.965202097.

Subproblem 1

x + -0.3333333334 = 7.965202097 Simplifying x + -0.3333333334 = 7.965202097 Reorder the terms: -0.3333333334 + x = 7.965202097 Solving -0.3333333334 + x = 7.965202097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 7.965202097 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 7.965202097 + 0.3333333334 x = 7.965202097 + 0.3333333334 Combine like terms: 7.965202097 + 0.3333333334 = 8.2985354304 x = 8.2985354304 Simplifying x = 8.2985354304

Subproblem 2

x + -0.3333333334 = -7.965202097 Simplifying x + -0.3333333334 = -7.965202097 Reorder the terms: -0.3333333334 + x = -7.965202097 Solving -0.3333333334 + x = -7.965202097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -7.965202097 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -7.965202097 + 0.3333333334 x = -7.965202097 + 0.3333333334 Combine like terms: -7.965202097 + 0.3333333334 = -7.6318687636 x = -7.6318687636 Simplifying x = -7.6318687636

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.2985354304, -7.6318687636}

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