3x^2+x-112=0

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Solution for 3x^2+x-112=0 equation:


Simplifying
3x2 + x + -112 = 0

Reorder the terms:
-112 + x + 3x2 = 0

Solving
-112 + 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'.
-37.33333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '37.33333333' to each side of the equation.
-37.33333333 + 0.3333333333x + 37.33333333 + x2 = 0 + 37.33333333

Reorder the terms:
-37.33333333 + 37.33333333 + 0.3333333333x + x2 = 0 + 37.33333333

Combine like terms: -37.33333333 + 37.33333333 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + 37.33333333
0.3333333333x + x2 = 0 + 37.33333333

Combine like terms: 0 + 37.33333333 = 37.33333333
0.3333333333x + x2 = 37.33333333

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 = 37.33333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 37.33333333 + 0.25

Combine like terms: 37.33333333 + 0.25 = 37.58333333
0.25 + 0.3333333333x + x2 = 37.58333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 37.58333333

Calculate the square root of the right side: 6.130524719

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.130524719 and -6.130524719.

Subproblem 1

x + 0.5 = 6.130524719 Simplifying x + 0.5 = 6.130524719 Reorder the terms: 0.5 + x = 6.130524719 Solving 0.5 + x = 6.130524719 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 = 6.130524719 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.130524719 + -0.5 x = 6.130524719 + -0.5 Combine like terms: 6.130524719 + -0.5 = 5.630524719 x = 5.630524719 Simplifying x = 5.630524719

Subproblem 2

x + 0.5 = -6.130524719 Simplifying x + 0.5 = -6.130524719 Reorder the terms: 0.5 + x = -6.130524719 Solving 0.5 + x = -6.130524719 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 = -6.130524719 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.130524719 + -0.5 x = -6.130524719 + -0.5 Combine like terms: -6.130524719 + -0.5 = -6.630524719 x = -6.630524719 Simplifying x = -6.630524719

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.630524719, -6.630524719}

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