3x^2=-8x-2

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


Simplifying
3x2 = -8x + -2

Reorder the terms:
3x2 = -2 + -8x

Solving
3x2 = -2 + -8x

Solving for variable 'x'.

Reorder the terms:
2 + 8x + 3x2 = -2 + -8x + 2 + 8x

Reorder the terms:
2 + 8x + 3x2 = -2 + 2 + -8x + 8x

Combine like terms: -2 + 2 = 0
2 + 8x + 3x2 = 0 + -8x + 8x
2 + 8x + 3x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
2 + 8x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 2.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 2.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 2.666666667x + x2 = 0 + -0.6666666667
2.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
2.666666667x + x2 = -0.6666666667

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 = -0.6666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -0.6666666667 + 1.777777780

Combine like terms: -0.6666666667 + 1.777777780 = 1.1111111133
1.777777780 + 2.666666667x + x2 = 1.1111111133

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 1.1111111133

Calculate the square root of the right side: 1.054092554

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.054092554 and -1.054092554.

Subproblem 1

x + 1.333333334 = 1.054092554 Simplifying x + 1.333333334 = 1.054092554 Reorder the terms: 1.333333334 + x = 1.054092554 Solving 1.333333334 + x = 1.054092554 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 = 1.054092554 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.054092554 + -1.333333334 x = 1.054092554 + -1.333333334 Combine like terms: 1.054092554 + -1.333333334 = -0.27924078 x = -0.27924078 Simplifying x = -0.27924078

Subproblem 2

x + 1.333333334 = -1.054092554 Simplifying x + 1.333333334 = -1.054092554 Reorder the terms: 1.333333334 + x = -1.054092554 Solving 1.333333334 + x = -1.054092554 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 = -1.054092554 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.054092554 + -1.333333334 x = -1.054092554 + -1.333333334 Combine like terms: -1.054092554 + -1.333333334 = -2.387425888 x = -2.387425888 Simplifying x = -2.387425888

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.27924078, -2.387425888}

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