.33333333333x^2+6x+10=0

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Solution for .33333333333x^2+6x+10=0 equation:


Simplifying
0.33333333333x2 + 6x + 10 = 0

Reorder the terms:
10 + 6x + 0.33333333333x2 = 0

Solving
10 + 6x + 0.33333333333x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.33333333333 the coefficient of the squared term: 

Divide each side by '0.33333333333'.
30 + 18x + x2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 18x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 18x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 18x + x2 = 0 + -30
18x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
18x + x2 = -30

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -30 + 81

Reorder the terms:
81 + 18x + x2 = -30 + 81

Combine like terms: -30 + 81 = 51
81 + 18x + x2 = 51

Factor a perfect square on the left side:
(x + 9)(x + 9) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + 9) equal to 7.141428429 and -7.141428429.

Subproblem 1

x + 9 = 7.141428429 Simplifying x + 9 = 7.141428429 Reorder the terms: 9 + x = 7.141428429 Solving 9 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 7.141428429 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.141428429 + -9 x = 7.141428429 + -9 Combine like terms: 7.141428429 + -9 = -1.858571571 x = -1.858571571 Simplifying x = -1.858571571

Subproblem 2

x + 9 = -7.141428429 Simplifying x + 9 = -7.141428429 Reorder the terms: 9 + x = -7.141428429 Solving 9 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -7.141428429 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.141428429 + -9 x = -7.141428429 + -9 Combine like terms: -7.141428429 + -9 = -16.141428429 x = -16.141428429 Simplifying x = -16.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.858571571, -16.141428429}

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