4x(3x-5)=2x+11

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Solution for 4x(3x-5)=2x+11 equation:


Simplifying
4x(3x + -5) = 2x + 11

Reorder the terms:
4x(-5 + 3x) = 2x + 11
(-5 * 4x + 3x * 4x) = 2x + 11
(-20x + 12x2) = 2x + 11

Reorder the terms:
-20x + 12x2 = 11 + 2x

Solving
-20x + 12x2 = 11 + 2x

Solving for variable 'x'.

Reorder the terms:
-11 + -20x + -2x + 12x2 = 11 + 2x + -11 + -2x

Combine like terms: -20x + -2x = -22x
-11 + -22x + 12x2 = 11 + 2x + -11 + -2x

Reorder the terms:
-11 + -22x + 12x2 = 11 + -11 + 2x + -2x

Combine like terms: 11 + -11 = 0
-11 + -22x + 12x2 = 0 + 2x + -2x
-11 + -22x + 12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-11 + -22x + 12x2 = 0

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

Divide each side by '12'.
-0.9166666667 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + -1.833333333x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + -1.833333333x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + -1.833333333x + x2 = 0 + 0.9166666667
-1.833333333x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
-1.833333333x + x2 = 0.9166666667

The x term is -1.833333333x.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333x + 0.8402777775 + x2 = 0.9166666667 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 0.9166666667 + 0.8402777775

Combine like terms: 0.9166666667 + 0.8402777775 = 1.7569444442
0.8402777775 + -1.833333333x + x2 = 1.7569444442

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 1.7569444442

Calculate the square root of the right side: 1.32549781

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 1.32549781 and -1.32549781.

Subproblem 1

x + -0.9166666665 = 1.32549781 Simplifying x + -0.9166666665 = 1.32549781 Reorder the terms: -0.9166666665 + x = 1.32549781 Solving -0.9166666665 + x = 1.32549781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 1.32549781 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.32549781 + 0.9166666665 x = 1.32549781 + 0.9166666665 Combine like terms: 1.32549781 + 0.9166666665 = 2.2421644765 x = 2.2421644765 Simplifying x = 2.2421644765

Subproblem 2

x + -0.9166666665 = -1.32549781 Simplifying x + -0.9166666665 = -1.32549781 Reorder the terms: -0.9166666665 + x = -1.32549781 Solving -0.9166666665 + x = -1.32549781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -1.32549781 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.32549781 + 0.9166666665 x = -1.32549781 + 0.9166666665 Combine like terms: -1.32549781 + 0.9166666665 = -0.4088311435 x = -0.4088311435 Simplifying x = -0.4088311435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.2421644765, -0.4088311435}

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