0.33333333333x^2+0.16666666666x=3

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Solution for 0.33333333333x^2+0.16666666666x=3 equation:


Simplifying
0.33333333333x2 + 0.16666666666x = 3

Reorder the terms:
0.16666666666x + 0.33333333333x2 = 3

Solving
0.16666666666x + 0.33333333333x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 0.16666666666x + 0.33333333333x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 0.16666666666x + 0.33333333333x2 = 0

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

Divide each side by '0.33333333333'.
-9 + 0.5x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 0.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 0.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 0.5x + x2 = 0 + 9
0.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
0.5x + x2 = 9

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 9 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 9 + 0.0625

Combine like terms: 9 + 0.0625 = 9.0625
0.0625 + 0.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + 0.25) equal to 3.010398645 and -3.010398645.

Subproblem 1

x + 0.25 = 3.010398645 Simplifying x + 0.25 = 3.010398645 Reorder the terms: 0.25 + x = 3.010398645 Solving 0.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.010398645 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.010398645 + -0.25 x = 3.010398645 + -0.25 Combine like terms: 3.010398645 + -0.25 = 2.760398645 x = 2.760398645 Simplifying x = 2.760398645

Subproblem 2

x + 0.25 = -3.010398645 Simplifying x + 0.25 = -3.010398645 Reorder the terms: 0.25 + x = -3.010398645 Solving 0.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.010398645 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.010398645 + -0.25 x = -3.010398645 + -0.25 Combine like terms: -3.010398645 + -0.25 = -3.260398645 x = -3.260398645 Simplifying x = -3.260398645

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.760398645, -3.260398645}

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