6.2=x(7.2-x)

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Solution for 6.2=x(7.2-x) equation: 


Simplifying
6.2 = x(7.2 + -1x)
6.2 = (7.2 * x + -1x * x)
6.2 = (7.2x + -1x2)

Solving
6.2 = 7.2x + -1x2

Solving for variable 'x'.

Reorder the terms:
6.2 + -7.2x + x2 = 7.2x + -7.2x + -1x2 + x2

Combine like terms: 7.2x + -7.2x = 0.0
6.2 + -7.2x + x2 = 0.0 + -1x2 + x2
6.2 + -7.2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
6.2 + -7.2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6.2' to each side of the equation.
6.2 + -7.2x + -6.2 + x2 = 0 + -6.2

Reorder the terms:
6.2 + -6.2 + -7.2x + x2 = 0 + -6.2

Combine like terms: 6.2 + -6.2 = 0.0
0.0 + -7.2x + x2 = 0 + -6.2
-7.2x + x2 = 0 + -6.2

Combine like terms: 0 + -6.2 = -6.2
-7.2x + x2 = -6.2

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = -6.2 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = -6.2 + 12.96

Combine like terms: -6.2 + 12.96 = 6.76
12.96 + -7.2x + x2 = 6.76

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 6.76

Calculate the square root of the right side: 2.6

Break this problem into two subproblems by setting 
(x + -3.6) equal to 2.6 and -2.6.


Subproblem 1
x + -3.6 = 2.6

Simplifying
x + -3.6 = 2.6

Reorder the terms:
-3.6 + x = 2.6

Solving
-3.6 + x = 2.6

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = 2.6 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = 2.6 + 3.6
x = 2.6 + 3.6

Combine like terms: 2.6 + 3.6 = 6.2
x = 6.2

Simplifying
x = 6.2


Subproblem 2
x + -3.6 = -2.6

Simplifying
x + -3.6 = -2.6

Reorder the terms:
-3.6 + x = -2.6

Solving
-3.6 + x = -2.6

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = -2.6 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = -2.6 + 3.6
x = -2.6 + 3.6

Combine like terms: -2.6 + 3.6 = 1
x = 1

Simplifying
x = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.2, 1}

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