5x(x-11)=8

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


Simplifying
5x(x + -11) = 8

Reorder the terms:
5x(-11 + x) = 8
(-11 * 5x + x * 5x) = 8
(-55x + 5x2) = 8

Solving
-55x + 5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -55x + 5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -55x + 5x2 = 0

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

Divide each side by '5'.
-1.6 + -11x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -11x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -11x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -11x + x2 = 0 + 1.6
-11x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-11x + x2 = 1.6

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 1.6 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 1.6 + 30.25

Combine like terms: 1.6 + 30.25 = 31.85
30.25 + -11x + x2 = 31.85

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 31.85

Calculate the square root of the right side: 5.643580424

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.643580424 and -5.643580424.

Subproblem 1

x + -5.5 = 5.643580424 Simplifying x + -5.5 = 5.643580424 Reorder the terms: -5.5 + x = 5.643580424 Solving -5.5 + x = 5.643580424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.643580424 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.643580424 + 5.5 x = 5.643580424 + 5.5 Combine like terms: 5.643580424 + 5.5 = 11.143580424 x = 11.143580424 Simplifying x = 11.143580424

Subproblem 2

x + -5.5 = -5.643580424 Simplifying x + -5.5 = -5.643580424 Reorder the terms: -5.5 + x = -5.643580424 Solving -5.5 + x = -5.643580424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.643580424 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.643580424 + 5.5 x = -5.643580424 + 5.5 Combine like terms: -5.643580424 + 5.5 = -0.143580424 x = -0.143580424 Simplifying x = -0.143580424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.143580424, -0.143580424}

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