4x(x-7)=2

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Solution for 4x(x-7)=2 equation: 


Simplifying
4x(x + -7) = 2

Reorder the terms:
4x(-7 + x) = 2
(-7 * 4x + x * 4x) = 2
(-28x + 4x2) = 2

Solving
-28x + 4x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -28x + 4x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -14x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -14x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -14x + 2x2 = 0

Solving
-1 + -14x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -7x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -7x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -7x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -7x + x2 = 0 + 0.5
-7x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-7x + x2 = 0.5

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 = 0.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 0.5 + 12.25

Combine like terms: 0.5 + 12.25 = 12.75
12.25 + -7x + x2 = 12.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.570714214 and -3.570714214.


Subproblem 1
x + -3.5 = 3.570714214

Simplifying
x + -3.5 = 3.570714214

Reorder the terms:
-3.5 + x = 3.570714214

Solving
-3.5 + x = 3.570714214

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 = 3.570714214 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.570714214 + 3.5
x = 3.570714214 + 3.5

Combine like terms: 3.570714214 + 3.5 = 7.070714214
x = 7.070714214

Simplifying
x = 7.070714214


Subproblem 2
x + -3.5 = -3.570714214

Simplifying
x + -3.5 = -3.570714214

Reorder the terms:
-3.5 + x = -3.570714214

Solving
-3.5 + x = -3.570714214

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 = -3.570714214 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.570714214 + 3.5
x = -3.570714214 + 3.5

Combine like terms: -3.570714214 + 3.5 = -0.070714214
x = -0.070714214

Simplifying
x = -0.070714214


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.070714214, -0.070714214}
Solution
x = {7.070714214, -0.070714214}

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