x(26-2x)=34

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Solution for x(26-2x)=34 equation: 


Simplifying
x(26 + -2x) = 34
(26 * x + -2x * x) = 34
(26x + -2x2) = 34

Solving
26x + -2x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 26x + -2x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 26x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 13x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + 13x + -1x2)' equal to zero and attempt to solve:

Simplifying
-17 + 13x + -1x2 = 0

Solving
-17 + 13x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
17 + -13x + x2 = 0

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -13x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -13x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -13x + x2 = 0 + -17
-13x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-13x + x2 = -17

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -17 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -17 + 42.25

Combine like terms: -17 + 42.25 = 25.25
42.25 + -13x + x2 = 25.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
x + -6.5 = 5.024937811

Simplifying
x + -6.5 = 5.024937811

Reorder the terms:
-6.5 + x = 5.024937811

Solving
-6.5 + x = 5.024937811

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 5.024937811 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 5.024937811 + 6.5
x = 5.024937811 + 6.5

Combine like terms: 5.024937811 + 6.5 = 11.524937811
x = 11.524937811

Simplifying
x = 11.524937811


Subproblem 2
x + -6.5 = -5.024937811

Simplifying
x + -6.5 = -5.024937811

Reorder the terms:
-6.5 + x = -5.024937811

Solving
-6.5 + x = -5.024937811

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -5.024937811 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -5.024937811 + 6.5
x = -5.024937811 + 6.5

Combine like terms: -5.024937811 + 6.5 = 1.475062189
x = 1.475062189

Simplifying
x = 1.475062189


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.524937811, 1.475062189}
Solution
x = {11.524937811, 1.475062189}

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