3x^2+3x-16=0

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Solution for 3x^2+3x-16=0 equation:


Simplifying
3x2 + 3x + -16 = 0

Reorder the terms:
-16 + 3x + 3x2 = 0

Solving
-16 + 3x + 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'.
-5.333333333 + x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + x + x2 = 0 + 5.333333333
x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
x + x2 = 5.333333333

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

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 5.333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 5.333333333 + 0.25

Combine like terms: 5.333333333 + 0.25 = 5.583333333
1.25 + x2 = 5.583333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.583333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.362907813 and -2.362907813.

Subproblem 1

x + 0.5 = 2.362907813 Simplifying x + 0.5 = 2.362907813 Reorder the terms: 0.5 + x = 2.362907813 Solving 0.5 + x = 2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.362907813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.362907813 + -0.5 x = 2.362907813 + -0.5 Combine like terms: 2.362907813 + -0.5 = 1.862907813 x = 1.862907813 Simplifying x = 1.862907813

Subproblem 2

x + 0.5 = -2.362907813 Simplifying x + 0.5 = -2.362907813 Reorder the terms: 0.5 + x = -2.362907813 Solving 0.5 + x = -2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.362907813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.362907813 + -0.5 x = -2.362907813 + -0.5 Combine like terms: -2.362907813 + -0.5 = -2.862907813 x = -2.862907813 Simplifying x = -2.862907813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.862907813, -2.862907813}

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