3x^2+12x-91=0

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Solution for 3x^2+12x-91=0 equation:


Simplifying
3x2 + 12x + -91 = 0

Reorder the terms:
-91 + 12x + 3x2 = 0

Solving
-91 + 12x + 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'.
-30.33333333 + 4x + x2 = 0

Move the constant term to the right:

Add '30.33333333' to each side of the equation.
-30.33333333 + 4x + 30.33333333 + x2 = 0 + 30.33333333

Reorder the terms:
-30.33333333 + 30.33333333 + 4x + x2 = 0 + 30.33333333

Combine like terms: -30.33333333 + 30.33333333 = 0.00000000
0.00000000 + 4x + x2 = 0 + 30.33333333
4x + x2 = 0 + 30.33333333

Combine like terms: 0 + 30.33333333 = 30.33333333
4x + x2 = 30.33333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 30.33333333 + 4

Reorder the terms:
4 + 4x + x2 = 30.33333333 + 4

Combine like terms: 30.33333333 + 4 = 34.33333333
4 + 4x + x2 = 34.33333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 34.33333333

Calculate the square root of the right side: 5.859465277

Break this problem into two subproblems by setting 
(x + 2) equal to 5.859465277 and -5.859465277.

Subproblem 1

x + 2 = 5.859465277 Simplifying x + 2 = 5.859465277 Reorder the terms: 2 + x = 5.859465277 Solving 2 + x = 5.859465277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.859465277 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.859465277 + -2 x = 5.859465277 + -2 Combine like terms: 5.859465277 + -2 = 3.859465277 x = 3.859465277 Simplifying x = 3.859465277

Subproblem 2

x + 2 = -5.859465277 Simplifying x + 2 = -5.859465277 Reorder the terms: 2 + x = -5.859465277 Solving 2 + x = -5.859465277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.859465277 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.859465277 + -2 x = -5.859465277 + -2 Combine like terms: -5.859465277 + -2 = -7.859465277 x = -7.859465277 Simplifying x = -7.859465277

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.859465277, -7.859465277}

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