x(x-24)-128=0

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Solution for x(x-24)-128=0 equation:


Simplifying
x(x + -24) + -128 = 0

Reorder the terms:
x(-24 + x) + -128 = 0
(-24 * x + x * x) + -128 = 0
(-24x + x2) + -128 = 0

Reorder the terms:
-128 + -24x + x2 = 0

Solving
-128 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + -24x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + -24x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + -24x + x2 = 0 + 128
-24x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
-24x + x2 = 128

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = 128 + 144

Reorder the terms:
144 + -24x + x2 = 128 + 144

Combine like terms: 128 + 144 = 272
144 + -24x + x2 = 272

Factor a perfect square on the left side:
(x + -12)(x + -12) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x + -12) equal to 16.492422502 and -16.492422502.

Subproblem 1

x + -12 = 16.492422502 Simplifying x + -12 = 16.492422502 Reorder the terms: -12 + x = 16.492422502 Solving -12 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 16.492422502 + 12 Combine like terms: -12 + 12 = 0 0 + x = 16.492422502 + 12 x = 16.492422502 + 12 Combine like terms: 16.492422502 + 12 = 28.492422502 x = 28.492422502 Simplifying x = 28.492422502

Subproblem 2

x + -12 = -16.492422502 Simplifying x + -12 = -16.492422502 Reorder the terms: -12 + x = -16.492422502 Solving -12 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -16.492422502 + 12 Combine like terms: -12 + 12 = 0 0 + x = -16.492422502 + 12 x = -16.492422502 + 12 Combine like terms: -16.492422502 + 12 = -4.492422502 x = -4.492422502 Simplifying x = -4.492422502

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.492422502, -4.492422502}

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