12x^2+11x-7=

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Solution for 12x^2+11x-7= equation:


Simplifying
12x2 + 11x + -7 = 0

Reorder the terms:
-7 + 11x + 12x2 = 0

Solving
-7 + 11x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-0.5833333333 + 0.9166666667x + x2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + 0.9166666667x + 0.5833333333 + x2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + 0.9166666667x + x2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + 0.9166666667x + x2 = 0 + 0.5833333333
0.9166666667x + x2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
0.9166666667x + x2 = 0.5833333333

The x term is 0.9166666667x.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667x + 0.2100694445 + x2 = 0.5833333333 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667x + x2 = 0.5833333333 + 0.2100694445

Combine like terms: 0.5833333333 + 0.2100694445 = 0.7934027778
0.2100694445 + 0.9166666667x + x2 = 0.7934027778

Factor a perfect square on the left side:
(x + 0.4583333334)(x + 0.4583333334) = 0.7934027778

Calculate the square root of the right side: 0.890731597

Break this problem into two subproblems by setting 
(x + 0.4583333334) equal to 0.890731597 and -0.890731597.

Subproblem 1

x + 0.4583333334 = 0.890731597 Simplifying x + 0.4583333334 = 0.890731597 Reorder the terms: 0.4583333334 + x = 0.890731597 Solving 0.4583333334 + x = 0.890731597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 0.890731597 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 0.890731597 + -0.4583333334 x = 0.890731597 + -0.4583333334 Combine like terms: 0.890731597 + -0.4583333334 = 0.4323982636 x = 0.4323982636 Simplifying x = 0.4323982636

Subproblem 2

x + 0.4583333334 = -0.890731597 Simplifying x + 0.4583333334 = -0.890731597 Reorder the terms: 0.4583333334 + x = -0.890731597 Solving 0.4583333334 + x = -0.890731597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -0.890731597 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -0.890731597 + -0.4583333334 x = -0.890731597 + -0.4583333334 Combine like terms: -0.890731597 + -0.4583333334 = -1.3490649304 x = -1.3490649304 Simplifying x = -1.3490649304

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4323982636, -1.3490649304}

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