3x^2+x-28=0

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Solution for 3x^2+x-28=0 equation:


Simplifying
3x2 + x + -28 = 0

Reorder the terms:
-28 + x + 3x2 = 0

Solving
-28 + x + 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'.
-9.333333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + 0.3333333333x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + 0.3333333333x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + 9.333333333
0.3333333333x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
0.3333333333x + x2 = 9.333333333

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.
0.3333333333x + 0.25 + x2 = 9.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 9.333333333 + 0.25

Combine like terms: 9.333333333 + 0.25 = 9.583333333
0.25 + 0.3333333333x + x2 = 9.583333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 9.583333333

Calculate the square root of the right side: 3.095695937

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.095695937 and -3.095695937.

Subproblem 1

x + 0.5 = 3.095695937 Simplifying x + 0.5 = 3.095695937 Reorder the terms: 0.5 + x = 3.095695937 Solving 0.5 + x = 3.095695937 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 = 3.095695937 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.095695937 + -0.5 x = 3.095695937 + -0.5 Combine like terms: 3.095695937 + -0.5 = 2.595695937 x = 2.595695937 Simplifying x = 2.595695937

Subproblem 2

x + 0.5 = -3.095695937 Simplifying x + 0.5 = -3.095695937 Reorder the terms: 0.5 + x = -3.095695937 Solving 0.5 + x = -3.095695937 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 = -3.095695937 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.095695937 + -0.5 x = -3.095695937 + -0.5 Combine like terms: -3.095695937 + -0.5 = -3.595695937 x = -3.595695937 Simplifying x = -3.595695937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.595695937, -3.595695937}

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