300=x(72-4x)

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Solution for 300=x(72-4x) equation: 


Simplifying
300 = x(72 + -4x)
300 = (72 * x + -4x * x)
300 = (72x + -4x2)

Solving
300 = 72x + -4x2

Solving for variable 'x'.

Reorder the terms:
300 + -72x + 4x2 = 72x + -72x + -4x2 + 4x2

Combine like terms: 72x + -72x = 0
300 + -72x + 4x2 = 0 + -4x2 + 4x2
300 + -72x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
300 + -72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(75 + -18x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(75 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
75 + -18x + x2 = 0

Solving
75 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + -18x + -75 + x2 = 0 + -75

Reorder the terms:
75 + -75 + -18x + x2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -18x + x2 = 0 + -75
-18x + x2 = 0 + -75

Combine like terms: 0 + -75 = -75
-18x + x2 = -75

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -75 + 81

Reorder the terms:
81 + -18x + x2 = -75 + 81

Combine like terms: -75 + 81 = 6
81 + -18x + x2 = 6

Factor a perfect square on the left side:
(x + -9)(x + -9) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -9) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + -9 = 2.449489743

Simplifying
x + -9 = 2.449489743

Reorder the terms:
-9 + x = 2.449489743

Solving
-9 + x = 2.449489743

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 2.449489743 + 9

Combine like terms: -9 + 9 = 0
0 + x = 2.449489743 + 9
x = 2.449489743 + 9

Combine like terms: 2.449489743 + 9 = 11.449489743
x = 11.449489743

Simplifying
x = 11.449489743


Subproblem 2
x + -9 = -2.449489743

Simplifying
x + -9 = -2.449489743

Reorder the terms:
-9 + x = -2.449489743

Solving
-9 + x = -2.449489743

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -2.449489743 + 9

Combine like terms: -9 + 9 = 0
0 + x = -2.449489743 + 9
x = -2.449489743 + 9

Combine like terms: -2.449489743 + 9 = 6.550510257
x = 6.550510257

Simplifying
x = 6.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.449489743, 6.550510257}
Solution
x = {11.449489743, 6.550510257}

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