25-11=2x(x-7)

Solution for 25-11=2x(x-7) equation:

Simplifying
25 + -11 = 2x(x + -7)

Combine like terms: 25 + -11 = 14
14 = 2x(x + -7)

Reorder the terms:
14 = 2x(-7 + x)
14 = (-7 * 2x + x * 2x)
14 = (-14x + 2x2)

Solving
14 = -14x + 2x2

Solving for variable 'x'.

Reorder the terms:
14 + 14x + -2x2 = -14x + 14x + 2x2 + -2x2

Combine like terms: -14x + 14x = 0
14 + 14x + -2x2 = 0 + 2x2 + -2x2
14 + 14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
14 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 7x + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + 7x + -1x2 = 0

Solving
7 + 7x + -1x2 = 0

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

Divide each side by '-1'.
-7 + -7x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -7x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -7x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -7x + x2 = 0 + 7
-7x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-7x + x2 = 7

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 7 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 7 + 12.25

Combine like terms: 7 + 12.25 = 19.25
12.25 + -7x + x2 = 19.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
x + -3.5 = 4.387482194

Simplifying
x + -3.5 = 4.387482194

Reorder the terms:
-3.5 + x = 4.387482194

Solving
-3.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.387482194 + 3.5
x = 4.387482194 + 3.5

Combine like terms: 4.387482194 + 3.5 = 7.887482194
x = 7.887482194

Simplifying
x = 7.887482194

Subproblem 2
x + -3.5 = -4.387482194

Simplifying
x + -3.5 = -4.387482194

Reorder the terms:
-3.5 + x = -4.387482194

Solving
-3.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.387482194 + 3.5
x = -4.387482194 + 3.5

Combine like terms: -4.387482194 + 3.5 = -0.887482194
x = -0.887482194

Simplifying
x = -0.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.887482194, -0.887482194}
Solution
x = {7.887482194, -0.887482194}