9.11(2.4-x)(0.6-x)=2x^2

Solution for 9.11(2.4-x)(0.6-x)=2x^2 equation:

Simplifying
9.11(2.4 + -1x)(0.6 + -1x) = 2x2

Multiply (2.4 + -1x) * (0.6 + -1x)
9.11(2.4(0.6 + -1x) + -1x * (0.6 + -1x)) = 2x2
9.11((0.6 * 2.4 + -1x * 2.4) + -1x * (0.6 + -1x)) = 2x2
9.11((1.44 + -2.4x) + -1x * (0.6 + -1x)) = 2x2
9.11(1.44 + -2.4x + (0.6 * -1x + -1x * -1x)) = 2x2
9.11(1.44 + -2.4x + (-0.6x + 1x2)) = 2x2

Combine like terms: -2.4x + -0.6x = -3x
9.11(1.44 + -3x + 1x2) = 2x2
(1.44 * 9.11 + -3x * 9.11 + 1x2 * 9.11) = 2x2
(13.1184 + -27.33x + 9.11x2) = 2x2

Solving
13.1184 + -27.33x + 9.11x2 = 2x2

Solving for variable 'x'.

Combine like terms: 9.11x2 + -2x2 = 7.11x2
13.1184 + -27.33x + 7.11x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
13.1184 + -27.33x + 7.11x2 = 0

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

Divide each side by '7.11'.
1.845063291 + -3.843881857x + x2 = 0

Move the constant term to the right:

Add '-1.845063291' to each side of the equation.
1.845063291 + -3.843881857x + -1.845063291 + x2 = 0 + -1.845063291

Reorder the terms:
1.845063291 + -1.845063291 + -3.843881857x + x2 = 0 + -1.845063291

Combine like terms: 1.845063291 + -1.845063291 = 0.000000000
0.000000000 + -3.843881857x + x2 = 0 + -1.845063291
-3.843881857x + x2 = 0 + -1.845063291

Combine like terms: 0 + -1.845063291 = -1.845063291
-3.843881857x + x2 = -1.845063291

The x term is -3.843881857x.  Take half its coefficient (-1.921940929).
Square it (3.693856935) and add it to both sides.

Add '3.693856935' to each side of the equation.
-3.843881857x + 3.693856935 + x2 = -1.845063291 + 3.693856935

Reorder the terms:
3.693856935 + -3.843881857x + x2 = -1.845063291 + 3.693856935

Combine like terms: -1.845063291 + 3.693856935 = 1.848793644
3.693856935 + -3.843881857x + x2 = 1.848793644

Factor a perfect square on the left side:
(x + -1.921940929)(x + -1.921940929) = 1.848793644

Calculate the square root of the right side: 1.359703513

Break this problem into two subproblems by setting 
(x + -1.921940929) equal to 1.359703513 and -1.359703513.

Subproblem 1
x + -1.921940929 = 1.359703513

Simplifying
x + -1.921940929 = 1.359703513

Reorder the terms:
-1.921940929 + x = 1.359703513

Solving
-1.921940929 + x = 1.359703513

Solving for variable 'x'.

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

Add '1.921940929' to each side of the equation.
-1.921940929 + 1.921940929 + x = 1.359703513 + 1.921940929

Combine like terms: -1.921940929 + 1.921940929 = 0.000000000
0.000000000 + x = 1.359703513 + 1.921940929
x = 1.359703513 + 1.921940929

Combine like terms: 1.359703513 + 1.921940929 = 3.281644442
x = 3.281644442

Simplifying
x = 3.281644442

Subproblem 2
x + -1.921940929 = -1.359703513

Simplifying
x + -1.921940929 = -1.359703513

Reorder the terms:
-1.921940929 + x = -1.359703513

Solving
-1.921940929 + x = -1.359703513

Solving for variable 'x'.

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

Add '1.921940929' to each side of the equation.
-1.921940929 + 1.921940929 + x = -1.359703513 + 1.921940929

Combine like terms: -1.921940929 + 1.921940929 = 0.000000000
0.000000000 + x = -1.359703513 + 1.921940929
x = -1.359703513 + 1.921940929

Combine like terms: -1.359703513 + 1.921940929 = 0.562237416
x = 0.562237416

Simplifying
x = 0.562237416

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.281644442, 0.562237416}