4x(11-2x)=10

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Solution for 4x(11-2x)=10 equation: 


Simplifying
4x(11 + -2x) = 10
(11 * 4x + -2x * 4x) = 10
(44x + -8x2) = 10

Solving
44x + -8x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 44x + -8x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 44x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 22x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 22x + -4x2)' equal to zero and attempt to solve:

Simplifying
-5 + 22x + -4x2 = 0

Solving
-5 + 22x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.25 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -5.5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -5.5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -5.5x + x2 = 0 + -1.25
-5.5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-5.5x + x2 = -1.25

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -1.25 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -1.25 + 7.5625

Combine like terms: -1.25 + 7.5625 = 6.3125
7.5625 + -5.5x + x2 = 6.3125

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 6.3125

Calculate the square root of the right side: 2.512468905

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.512468905 and -2.512468905.


Subproblem 1
x + -2.75 = 2.512468905

Simplifying
x + -2.75 = 2.512468905

Reorder the terms:
-2.75 + x = 2.512468905

Solving
-2.75 + x = 2.512468905

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 2.512468905 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.512468905 + 2.75
x = 2.512468905 + 2.75

Combine like terms: 2.512468905 + 2.75 = 5.262468905
x = 5.262468905

Simplifying
x = 5.262468905


Subproblem 2
x + -2.75 = -2.512468905

Simplifying
x + -2.75 = -2.512468905

Reorder the terms:
-2.75 + x = -2.512468905

Solving
-2.75 + x = -2.512468905

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -2.512468905 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.512468905 + 2.75
x = -2.512468905 + 2.75

Combine like terms: -2.512468905 + 2.75 = 0.237531095
x = 0.237531095

Simplifying
x = 0.237531095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.262468905, 0.237531095}
Solution
x = {5.262468905, 0.237531095}

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