7x(-2x+11)=14

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Solution for 7x(-2x+11)=14 equation: 


Simplifying
7x(-2x + 11) = 14

Reorder the terms:
7x(11 + -2x) = 14
(11 * 7x + -2x * 7x) = 14
(77x + -14x2) = 14

Solving
77x + -14x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 77x + -14x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 77x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + 11x + -2x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-2 + 11x + -2x2)' equal to zero and attempt to solve:

Simplifying
-2 + 11x + -2x2 = 0

Solving
-2 + 11x + -2x2 = 0

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

Divide each side by '-2'.
1 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -5.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5.5x + x2 = 0 + -1
-5.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5.5x + x2 = -1

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 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -1 + 7.5625

Combine like terms: -1 + 7.5625 = 6.5625
7.5625 + -5.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.561737691 and -2.561737691.


Subproblem 1
x + -2.75 = 2.561737691

Simplifying
x + -2.75 = 2.561737691

Reorder the terms:
-2.75 + x = 2.561737691

Solving
-2.75 + x = 2.561737691

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 = 2.561737691 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.561737691 + 2.75
x = 2.561737691 + 2.75

Combine like terms: 2.561737691 + 2.75 = 5.311737691
x = 5.311737691

Simplifying
x = 5.311737691


Subproblem 2
x + -2.75 = -2.561737691

Simplifying
x + -2.75 = -2.561737691

Reorder the terms:
-2.75 + x = -2.561737691

Solving
-2.75 + x = -2.561737691

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 = -2.561737691 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.561737691 + 2.75
x = -2.561737691 + 2.75

Combine like terms: -2.561737691 + 2.75 = 0.188262309
x = 0.188262309

Simplifying
x = 0.188262309


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.311737691, 0.188262309}
Solution
x = {5.311737691, 0.188262309}

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