400=x(2x-6)

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Solution for 400=x(2x-6) equation: 


Simplifying
400 = x(2x + -6)

Reorder the terms:
400 = x(-6 + 2x)
400 = (-6 * x + 2x * x)
400 = (-6x + 2x2)

Solving
400 = -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
400 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
400 + 6x + -2x2 = 0 + 2x2 + -2x2
400 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
400 + 6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + 3x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(200 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
200 + 3x + -1x2 = 0

Solving
200 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-200 + -3x + x2 = 0

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -3x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + -3x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -3x + x2 = 0 + 200
-3x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
-3x + x2 = 200

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 200 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 200 + 2.25

Combine like terms: 200 + 2.25 = 202.25
2.25 + -3x + x2 = 202.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + -1.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
x + -1.5 = 14.221462653

Simplifying
x + -1.5 = 14.221462653

Reorder the terms:
-1.5 + x = 14.221462653

Solving
-1.5 + x = 14.221462653

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 14.221462653 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 14.221462653 + 1.5
x = 14.221462653 + 1.5

Combine like terms: 14.221462653 + 1.5 = 15.721462653
x = 15.721462653

Simplifying
x = 15.721462653


Subproblem 2
x + -1.5 = -14.221462653

Simplifying
x + -1.5 = -14.221462653

Reorder the terms:
-1.5 + x = -14.221462653

Solving
-1.5 + x = -14.221462653

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -14.221462653 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -14.221462653 + 1.5
x = -14.221462653 + 1.5

Combine like terms: -14.221462653 + 1.5 = -12.721462653
x = -12.721462653

Simplifying
x = -12.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.721462653, -12.721462653}
Solution
x = {15.721462653, -12.721462653}

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