2x(x-7)=28

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Solution for 2x(x-7)=28 equation: 


Simplifying
2x(x + -7) = 28

Reorder the terms:
2x(-7 + x) = 28
(-7 * 2x + x * 2x) = 28
(-14x + 2x2) = 28

Solving
-14x + 2x2 = 28

Solving for variable 'x'.

Reorder the terms:
-28 + -14x + 2x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + -7x + x2 = 0

Solving
-14 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -7x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -7x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -7x + x2 = 0 + 14
-7x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-7x + x2 = 14

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 = 14 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 14 + 12.25

Combine like terms: 14 + 12.25 = 26.25
12.25 + -7x + x2 = 26.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
x + -3.5 = 5.123475383

Simplifying
x + -3.5 = 5.123475383

Reorder the terms:
-3.5 + x = 5.123475383

Solving
-3.5 + x = 5.123475383

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 = 5.123475383 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 5.123475383 + 3.5
x = 5.123475383 + 3.5

Combine like terms: 5.123475383 + 3.5 = 8.623475383
x = 8.623475383

Simplifying
x = 8.623475383


Subproblem 2
x + -3.5 = -5.123475383

Simplifying
x + -3.5 = -5.123475383

Reorder the terms:
-3.5 + x = -5.123475383

Solving
-3.5 + x = -5.123475383

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 = -5.123475383 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -5.123475383 + 3.5
x = -5.123475383 + 3.5

Combine like terms: -5.123475383 + 3.5 = -1.623475383
x = -1.623475383

Simplifying
x = -1.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.623475383, -1.623475383}
Solution
x = {8.623475383, -1.623475383}

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