400=x(x-6)

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


Simplifying
400 = x(x + -6)

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

Solving
400 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
400 + 6x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
400 + 6x + -1x2 = 0 + x2 + -1x2
400 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
400 + 6x + -1x2 = 0

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

Divide each side by '-1'.
-400 + -6x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -6x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -6x + x2 = 0 + 400

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

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

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 400 + 9

Reorder the terms:
9 + -6x + x2 = 400 + 9

Combine like terms: 400 + 9 = 409
9 + -6x + x2 = 409

Factor a perfect square on the left side:
(x + -3)(x + -3) = 409

Calculate the square root of the right side: 20.223748416

Break this problem into two subproblems by setting 
(x + -3) equal to 20.223748416 and -20.223748416.

Subproblem 1

x + -3 = 20.223748416 Simplifying x + -3 = 20.223748416 Reorder the terms: -3 + x = 20.223748416 Solving -3 + x = 20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 20.223748416 + 3 Combine like terms: -3 + 3 = 0 0 + x = 20.223748416 + 3 x = 20.223748416 + 3 Combine like terms: 20.223748416 + 3 = 23.223748416 x = 23.223748416 Simplifying x = 23.223748416

Subproblem 2

x + -3 = -20.223748416 Simplifying x + -3 = -20.223748416 Reorder the terms: -3 + x = -20.223748416 Solving -3 + x = -20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -20.223748416 + 3 Combine like terms: -3 + 3 = 0 0 + x = -20.223748416 + 3 x = -20.223748416 + 3 Combine like terms: -20.223748416 + 3 = -17.223748416 x = -17.223748416 Simplifying x = -17.223748416

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.223748416, -17.223748416}

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