12x(x+8)=11x-5

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Solution for 12x(x+8)=11x-5 equation:


Simplifying
12x(x + 8) = 11x + -5

Reorder the terms:
12x(8 + x) = 11x + -5
(8 * 12x + x * 12x) = 11x + -5
(96x + 12x2) = 11x + -5

Reorder the terms:
96x + 12x2 = -5 + 11x

Solving
96x + 12x2 = -5 + 11x

Solving for variable 'x'.

Reorder the terms:
5 + 96x + -11x + 12x2 = -5 + 11x + 5 + -11x

Combine like terms: 96x + -11x = 85x
5 + 85x + 12x2 = -5 + 11x + 5 + -11x

Reorder the terms:
5 + 85x + 12x2 = -5 + 5 + 11x + -11x

Combine like terms: -5 + 5 = 0
5 + 85x + 12x2 = 0 + 11x + -11x
5 + 85x + 12x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
5 + 85x + 12x2 = 0

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

Divide each side by '12'.
0.4166666667 + 7.083333333x + x2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + 7.083333333x + -0.4166666667 + x2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + 7.083333333x + x2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + 7.083333333x + x2 = 0 + -0.4166666667
7.083333333x + x2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
7.083333333x + x2 = -0.4166666667

The x term is 7.083333333x.  Take half its coefficient (3.541666667).
Square it (12.54340278) and add it to both sides.

Add '12.54340278' to each side of the equation.
7.083333333x + 12.54340278 + x2 = -0.4166666667 + 12.54340278

Reorder the terms:
12.54340278 + 7.083333333x + x2 = -0.4166666667 + 12.54340278

Combine like terms: -0.4166666667 + 12.54340278 = 12.1267361133
12.54340278 + 7.083333333x + x2 = 12.1267361133

Factor a perfect square on the left side:
(x + 3.541666667)(x + 3.541666667) = 12.1267361133

Calculate the square root of the right side: 3.482346352

Break this problem into two subproblems by setting 
(x + 3.541666667) equal to 3.482346352 and -3.482346352.

Subproblem 1

x + 3.541666667 = 3.482346352 Simplifying x + 3.541666667 = 3.482346352 Reorder the terms: 3.541666667 + x = 3.482346352 Solving 3.541666667 + x = 3.482346352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.541666667' to each side of the equation. 3.541666667 + -3.541666667 + x = 3.482346352 + -3.541666667 Combine like terms: 3.541666667 + -3.541666667 = 0.000000000 0.000000000 + x = 3.482346352 + -3.541666667 x = 3.482346352 + -3.541666667 Combine like terms: 3.482346352 + -3.541666667 = -0.059320315 x = -0.059320315 Simplifying x = -0.059320315

Subproblem 2

x + 3.541666667 = -3.482346352 Simplifying x + 3.541666667 = -3.482346352 Reorder the terms: 3.541666667 + x = -3.482346352 Solving 3.541666667 + x = -3.482346352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.541666667' to each side of the equation. 3.541666667 + -3.541666667 + x = -3.482346352 + -3.541666667 Combine like terms: 3.541666667 + -3.541666667 = 0.000000000 0.000000000 + x = -3.482346352 + -3.541666667 x = -3.482346352 + -3.541666667 Combine like terms: -3.482346352 + -3.541666667 = -7.024013019 x = -7.024013019 Simplifying x = -7.024013019

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.059320315, -7.024013019}

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