x(15-2x)=11

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Solution for x(15-2x)=11 equation: 


Simplifying
x(15 + -2x) = 11
(15 * x + -2x * x) = 11
(15x + -2x2) = 11

Solving
15x + -2x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 15x + -2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 15x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
5.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -7.5x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -7.5x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -7.5x + x2 = 0 + -5.5
-7.5x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-7.5x + x2 = -5.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -5.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -5.5 + 14.0625

Combine like terms: -5.5 + 14.0625 = 8.5625
14.0625 + -7.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -3.75) equal to 2.926174978 and -2.926174978.


Subproblem 1
x + -3.75 = 2.926174978

Simplifying
x + -3.75 = 2.926174978

Reorder the terms:
-3.75 + x = 2.926174978

Solving
-3.75 + x = 2.926174978

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 2.926174978 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 2.926174978 + 3.75
x = 2.926174978 + 3.75

Combine like terms: 2.926174978 + 3.75 = 6.676174978
x = 6.676174978

Simplifying
x = 6.676174978


Subproblem 2
x + -3.75 = -2.926174978

Simplifying
x + -3.75 = -2.926174978

Reorder the terms:
-3.75 + x = -2.926174978

Solving
-3.75 + x = -2.926174978

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -2.926174978 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -2.926174978 + 3.75
x = -2.926174978 + 3.75

Combine like terms: -2.926174978 + 3.75 = 0.823825022
x = 0.823825022

Simplifying
x = 0.823825022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.676174978, 0.823825022}

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